This section of Chapter 1 has seven verses:

2 Timothy 1:1-7
1 Paul, an apostle of Jesus Christ by the will of God, according to the promise of life which is in Christ Jesus,
 2 To Timothy, my dearly beloved son: Grace, mercy, and peace, from God the Father and Christ Jesus our Lord.
 3 I thank God, whom I serve from my forefathers with pure conscience, that without ceasing I have remembrance of thee in my prayers night and day;
 4 Greatly desiring to see thee, being mindful of thy tears, that I may be filled with joy;
 5 When I call to remembrance the unfeigned faith that is in thee, which dwelt first in thy grandmother Lois, and thy mother Eunice; and I am persuaded that in thee also.
 6 Wherefore I put thee in remembrance that thou stir up the gift of God, which is in thee by the putting on of my hands.
 7 For God hath not given us the spirit of fear; but of power, and of love, and of a sound mind.

Let us begin with the Barclay commentary

AN APOSTLE’S GLORY AND AN APOSTLE’S PRIVILEGE

First, the paraphrase of the verses:

2 Timothy 1:1–7
This is a letter from Paul, who was made an apostle of Christ Jesus by the will of God, and whose apostleship was designed to make known to all men God’s promise of real life in Christ Jesus, to Timothy his own beloved child. Grace, mercy and peace be to you from God, the Father, and from Christ Jesus, our Lord.

I thank God, whom I serve with a clear conscience, as my forefathers did before me, for all that you are to me, just as in my prayers I never cease to remember you, for, remembering your tears when we parted, I never cease to yearn to see you, that I may be filled with joy. And I thank God that I have received a fresh reminder of that sincere faith which is in you, a faith of the same kind as first dwelt in your grandmother Lois and in your mother Eunice, and which, I am convinced, dwells in you too. That is why I send you this reminder to keep at white heat the gift that is in you and which came to you through the laying of my hands upon you; for God did not give us the spirit of craven fear, but of power and love and self-discipline.

WHEN Paul speaks of his own apostleship, there are always certain unmistakable notes in his voice. To Paul, his apostleship always meant certain things.

(1) His apostleship was an honour. He was chosen for it by the will of God. All Christians must regard themselves as God-chosen men and women.

(2) His apostleship was a responsibility. God chose him because he wanted to do something with him. He wanted to make him the instrument by which the tidings of new life went out to all people. Christians are never chosen entirely for their own sake, but for what they can do for others.  Christians are people who are lost in wonder, love and praise at what God has done for them and aflame with eagerness to tell others what God can do for them too.

(3) His apostleship was a privilege. It is most significant to see what Paul believed it his duty to bring to others – God’s promise, not his threat. To Paul, Christianity was not the threat of damnation; it was the good news of salvation.  It is worth remembering that the greatest evangelist and missionary the world has ever seen was out not to terrify people by shaking them over the flames of hellfire but to move them to astonished submission at the sight of the love of God. The driving force of his gospel was love, not fear.

As always when he speaks to Timothy, there is a warmth of loving affection in Paul’s voice. ‘My beloved child’, he calls him. Timothy was his child in the faith. Timothy’s parents had given him physical life, but it was Paul who gave him [instruction to] eternal life. Many people who never knew physical parenthood have had the joy and privilege of being a father or a mother in the faith.

PAUL’S object in writing is to inspire and strengthen Timothy for his task in Ephesus. Timothy was young, and he had a hard task in battling against the heresies and the infections that were bound to threaten the Church. So, in order to keep his courage high and his effort strenuous, Paul reminds Timothy of certain things.

(1) He reminds him of his own confidence in him. There is no greater inspiration than to feel that someone believes in us. An appeal to the best in someone is always more effective than a threat of punishment. The fear of letting down those who love us is a sobering thing.

(2) He reminds him of his family tradition. Timothy was walking in a fine heritage; and, if he failed, not only would he damage his own reputation but he would lessen the honour of his family name as well. A fine parentage is one of the greatest gifts anyone can have. It is something to thank God for and should never be dishonored. [See Deuteronomy 27:16]

Quoted verse:
Deuteronomy 27:16
Cursed be he that setteth light by his father or his mother. And all the people shall say, Amen.

(3) He reminds him of his setting apart for office and of the gift which was conferred upon him. Once we enter upon the service of any association with a tradition, anything that we do affects not only us. We do not do it in our own strength.  There is the strength of a tradition to draw upon and the honour of a tradition to preserve. That is especially true of the Church.  Those who serve it have its honour in their hands; those who serve it are strengthened by the consciousness of the [spiritual fellowship] of all the saints.

(4) He reminds him of the qualities which should characterize the Christian teacher. These, as Paul at that moment saw them, were four.

(a) There was courage. It was not cowardly fear but courage that Christian service should bring. It always takes courage to be a Christian, and that courage comes from the continual consciousness of the presence of Christ.

(b) There was power. In true Christians, there is the power to cope, the power to shoulder the backbreaking task, the power to stand firm when faced with the shattering situation, the power to retain faith when confronted by the soul-destroying sorrow and the wounding disappointment.  Christians are characteristically people who could pass the breaking point and not break.

(c) There was love. In Timothy’s case, this was love for the brothers and sisters, for the congregation of the people of Christ over whom he was set. It is precisely that love which gives Christian pastors other qualities. They must love their people so much that they will never find any toil too great to undertake for them or any situation threatening enough to daunt them. No one should ever enter the ministry of the Church without a deep love for Christ’s people.

(d) There was self-discipline. The word is so¯phronismos, one of these great untranslatable Greek words. It has been defined as ‘the sanity of saintliness’. In his book on The Pastorals, Sir Robert Falconer defines it as ‘control of oneself in face of panic or of passion’. It is Christ alone who can give us that command of self which will keep us both from being swept away and from running away.  No one can ever rule others without having complete self-control.  So¯phronismos is that divinely given control of self which makes people great rulers of others because they are first of all the servants of Christ and in complete control of themselves [by the power of the Holy Spirit]. ~Barclay Commentary

Now to the other commentaries.

We will begin with the general commentaries and move to the more specific. Here is part of the commentary on verses 6-14 from the Matthew Henry Concise:

God has not given us the spirit of fear, but the spirit of power, of courage and resolution, to meet difficulties and dangers; the spirit of love to him, which will carry us through opposition. And the spirit of a sound mind, quietness of mind. The Holy Spirit is not the author of a timid or cowardly disposition, or of slavish fears. We are likely to bear afflictions well, when we have strength and power from God to enable us to bear them. As is usual with Paul, when he mentions Christ and his redemption, he enlarges upon them; so full was he of that which is all our salvation, and ought to be all our desire. The call of the gospel is a holy call, making holy. Salvation is of free grace. This is said to be given us before the world began, that is, in the purpose of God from all eternity; in Christ Jesus, for all the gifts that come from God to sinful man, come in and through Christ Jesus alone. And as there is so clear a prospect of eternal happiness by faith in Him, who is the Resurrection and the Life, let us give more diligence in making his salvation sure to our souls. Those who cleave to the gospel, need not be ashamed, the cause will bear them out; but those who oppose it, shall be ashamed. ~Matthew Henry Concise

Now part of the commentary on verses 6-14 from the main Matthew Henry:

Here is an exhortation and excitation of Timothy to his duty (2 Timothy 1:6): I put thee in remembrance. The best men need remembrancers; what we know we should be reminded of. 2 Peter 3:1, I write this, to stir up your pure minds by way of remembrance.

I. He exhorts him to stir up the gift of God that was in him. Stir it up as fire under the embers. It is meant of all the gifts and graces the God had given him, to qualify him for the work of an evangelist, the gifts of the Holy Ghost, the extraordinary gifts that were conferred by the imposition of the apostle's hands. These he must stir up; he must exercise them and so increase them: use gifts and have gifts. To him that hath shall be given, Matthew 25:29. He must take all opportunities to use these gifts, and so stir them up, for that is the best way of increasing them. Whether the gift of God in Timothy was ordinary or extraordinary (though I incline to the latter), he must stir it up, otherwise it would decay. ~Matthew Henry main

Now notice the Biblical Illustrator which takes on the scripture by subject heading as opposed to word or phrase;

Stir up the gift of God which is in thee by the putting on of my hands.

The graces of God’s Spirit are of a fiery quality
And here we must all learn a double lesson. First, to get this fire; and next, to keep it from quenching. This is that one thing necessary; and how should we rejoice if it be already kindled! For without it we are blind, corrupt, cold, yea, stark dead. We must make our hearts the hearth to uphold it, and our hands the tongs to build it; it must lodge with us daily, send out flame from us, and our lamps must be continually burning; then shall we glorify our God, give light to others, walk safely, as walled about with a defence of fire, in this pilgrimage; and the Lord, at length, shall send us fiery chariots to carry us to [the Kingdom], where our lamps shall burn day and night, and shine as the sun in the clear firmament for ever and ever.

The gifts of God are to be stirred up within us
For if they be not, will they not perish? Have you not heard that they are of a fiery quality, and therefore subject, without stirring, blowing, to decay and be extinguished? The things that put out the fire of the spirit in us, are—first, evil cogitations; as smoke weakeneth the eye, cold frosts nip the tender bud, and stinking smells damp and dull the purest spirits, so do bad thoughts disturb, impoverish, and enfeeble the gifts of God that be in us. [Secondly, corrupt speech; that troubleth the fountain, and stoppeth the spirit’s spring; it shakes the young plants of grace, as the boisterous winds do the late grafted scions: this will cause the new man to die before his time, and the best fruits he beareth to become blasted. Thirdly, wicked works; they raze the foundation, and, like the boar of the wood, root up all; when these break forth into action, then falls grace suddenly into a consumption; for they do not only wither the branches and change the complexion, but also kill the body, devour the juice of life, and destroy the constitution. Fourthly, loud company; this doth press down and keep under the gifts of God, that they cannot shoot up and spring; as water to fire, green wood to dry, this quencheth all; one grain of this leaven leaveneth the whole lump. Let the Israelites live among the Egyptians, though they hate the men, yet they will learn their manners; and Peter will grow cold if he warm his fingers at Caiaphas’ fire. Fifthly, the prosperity of the wicked; that will buffet the soul, wound the very spirit, and make grace to look pale and wan. How have the faithful fainted to see this, and the strongest foot of faith reeled, staggered! This mud hath made the men of God almost to turn out of the way. Sixthly, and finally, the pampering of the flesh. It will impoverish the spirit, and make it look lank and lean. If the one be cherished, the other will be starved. When one of these buckets is ascending the other is descending. Paul knew it well, therefore would beat down his body, and keep it in subjection. These be the greatest impediments that hinder the gifts of grace from stirring, growing.

Private helps to stir up grace
First, reading either the Scriptures or other holy writings. This being done in a corner will refresh the spirit. It is like food to the fainting passenger. Secondly, meditation. He that sits long by the fire shall have his body to grow hot, and his cold spirits to become active, nimble. Let this be done thoroughly, and it will make grace to stretch itself beyond its ordinary wont, and the Christian to be rapt out of himself. Thirdly, prayer. Who ever in his secret chamber went to God by earnest prayer but he was ravished in mind, and in the strength of that action spent all that day without weariness? God giveth the greatest gifts in secret; and, like man, revealeth Himself apart. Yea, private prayer doth both stir up and increase grace mightily; and as secret meals make a fat body, so doth that a well-liking mind. Fourthly, observation, and that of the daily acts of God’s providence. Fifthly, examples: not the worst, but the most excellent. Set before thine eyes the cloud of witnesses, that have far outstripped thee. Think what a shame it is for thee to come so far behind them. Will not a comely suite make some leap into the fashion? Sixthly, resolution; which must consist in propounding to ourselves a higher pitch of perfection. He that would shoot or leap further than before will cast his eye and aim beyond the mark. But if all these will not stir up this fire, then consider what a loss it is to be a dwarf and bankrupt in this grace. How God may forsake us, an evil spirit possess us, and Satan seek about to apprehend us, as the Philistines did Samson; so shall we pluck up our spirits, stir up our strength, rise out of this lethargy, and fly for our lives.

The ordinances of God are not without profit, if rightly practiced
It is not a trade, but the well using of it; not a farm, but the well husbandry of it, that will enrich the one and the other. Wherefore, be steadfast, immoveable, and abundant in the work of the Lord, knowing that your labour is not in vain in the Lord.

Grounds of Paul’s appeal to Timothy
In encouraging Timothy to stir up the gift that is in him, and not suffer himself to be ashamed of the ignominy, or afraid of the hardships, which the service of Christ entails, the apostle puts before him five considerations. There are the beautiful traditions of his family, which are now in his keeping. There is the sublime character of the gospel which has been entrusted to him. There is the teaching of Paul himself, who has so often given him a “pattern of sound words” and a pattern of steadfast endurance. There is the example of Onesiphorus with his courageous devotion. And there is the sure hope of “the salvation which is in Christ Jesus with eternal glory.” Any one of these might suffice to influence him.

Watching the heart flame
The Greek word rendered “stir up” literally means to kindle up, to fan into flame. We know that Paul frequently uses for his illustrations of Christian life scenes well known among the Greek heathen nations of the Old World, such as the Greek athletic games. Is it not possible that the apostle while here charring Timothy to take care that the sacred fire of the Holy Spirit did not languish in his heart, while urging him to watch the flame, to keep it burning brightly, to fan the flame if burning dimly.

Individual gifts
What if God should command the flowers to appear before Him, and the sunflower should come bending low with shame because it was not a violet, and the violet should come striving to lift itself up to be like a sunflower, and the lily should seek to gain the bloom of the rose, and the rose the whiteness of the lily; and so, each one disdaining itself, should seek to grow into the likeness of the other? God would say, “Stop foolish flowers! I gave you your own forms and hues, and odours, and I wish you to bring what you have received. O sunflower, come as a sunflower; and you sweet violet, come as a violet; let the rose bring the rose’s bloom, and the lily the lily’s whiteness.”

Self-education
Every man has two educations—that which is given to him, and that which he gives himself. Of the two kinds, the latter is by far the most valuable. Indeed, till that is most worthy in a man, he must work out and conquer for himself. It is this that constitutes our real and best nourishment. What we are merely taught seldom nourishes the mind like that which we teach ourselves. ~Biblical Illustrator

Now to the specific commentaries, which take the scripture phrase by phrase and sometimes word by word.

Generally we have three phrases here:

1] Wherefore I put thee in remembrance.
2] That thou stir up the gift of God.
3] Which is in thee by the putting on of my hands.

1] Wherefore I put thee in remembrance.

Wherefore I put thee in remembrance - From the earnestness with which he stirs up Timothy in both Epistles, it seems likely that he did not possess the rugged, restless energy of Paul. ~People's New Testament

Wherefore I put thee in remembrance - He urges us to set the invincible power of the Spirit which God has given us, against those storms which may, and do come upon us. ~Geneva Notes

Wherefore I put thee in remembrance - Because of the great affection the apostle had for Timothy, and because of that confidence he had of him, that unfeigned faith dwelt in him, as well as because this had had a place in his relations before him; he therefore acts the part of a kind monitor to him, and, upon these considerations, doubts not of succeeding in his following admonition: ~John Gill

Wherefore I put thee in remembrance - Wherefore — Greek, “For which cause,” namely, because thou hast inherited, didst once possess, and I trust (“am persuaded”) still dost possess, such unfeigned faith ~Jamieson, Fausset, Brown

2] That thou stir up the gift of God.

Stir up the gift of God. - The supernatural gift which he received by the imposition of the apostolic hands. The gift of office was conferred by ordination at the hands of the presbytery; the gift of miraculous powers, by the imposition of the hands of an apostle. ~People's New Testament

That thou stir up the gift of God - Greek, That thou “kindle up” as a fire. The original word used here denotes the kindling of a fire, as by bellows, etc. It is not uncommon to compare piety to a flame or a fire, and the image is one that is obvious when we speak of causing that to burn more brightly. The idea is, that Timothy was to use all proper means to keep the flame of pure religion in the soul burning, and more particularly his zeal in the great cause to which he had been set apart. The agency of man himself is needful to keep the religion of the heart warm and glowing. However rich the gifts which God has bestowed upon us, they do not grow of their own accord, but need to be cultivated by our own personal care. ~Barnes Notes

Stir up the gift of God, which is in thee - The gift which Timothy had received was the Holy Spirit; and through him, a particular power to preach and defend the truth. This gift is represented here, under the notion of a fire, which, if it be not frequently stirred up, and fresh fuel added to it, will go out. This is the precise idea which the apostle had in his mind; hence the term αναζωπυρειν, which signifies to stir up the fire; to add fresh fuel to it. From this it plainly appears, that if Timothy had not continued to be a daily worker with God, he would have received the grace of God in vain. The Latins have a similar metaphor, excitare igniculos ingenii, to stir up the sparks of genius. ~Adam Clarke

Stir up the gift of God, which is in thee - The gift of God is as it were a certain living flame kindled in our hearts, which the flesh and the devil go about to put out: and therefore we as their opponents must labour as much as we can to foster and keep it burning. ~Geneva Notes

That thou stir up the gift of God which is in thee - by "the gift" is meant his ministerial gift; for what qualifies men for the ministry, is not anything natural in them, nor acquired by them, but what is given unto them, and that of God: and this was "in" him; it continued with him; it was not lost by him, nor taken from him, as gifts may be, when they are not used; and yet it seems as if there was some decline, some backwardness and indifference as to the exercise of it: he might be too remiss, negligent, and forgetful of it; wherefore the apostle puts him in mind to "stir" it up: there is in the word used a metaphor taken from coals of fire covered with ashes, as if almost extinct, and need to be blown up into a flame, and a very apt one it is; since the gifts of the Spirit, especially his extraordinary ones, such as ministers in those times had, are compared to fire: see Matthew 3:11 and these may be reinflamed or increased, when they seem on the decline, by reading, meditation, prayer, and the frequent exercise of them. Agreeably to this the Arabic version renders it, "that thou kindle the fire of the gift of God which is in thee"; and the rather the apostle took this freedom with Timothy, not only because of his superior age and office, but because this gift was through his means. ~John Gill

Quoted verse:
Matthew 3:11
I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire:

Stir up — literally, “rekindle,” “revive the spark of”; the opposite of “quench” or “extinguish” (1 Thessalonians 5:19). Paul does not doubt the existence of real faith in Timothy, but he desires it to be put into active exercise. Timothy seems to have become somewhat remiss from being so long without Paul (2 Timothy 2:22). ~Jamieson, Fausset, Brown

Quoted verses:
1 Thessalonians 5:19
Quench not the Spirit.

2 Timothy 2:22 [see lesson]
Flee also youthful lusts: but follow righteousness, faith, charity, peace, with them that call on the Lord out of a pure heart.

Gift of God — the spiritual grace received for his ministerial office, either at his original ordination, or at his consecration to the particular office of superintending the Ephesian Church (see on 1 Timothy 4:14), imparting fearlessness, power, love, and a sound mind (2 Timothy 1:7). ~Jamieson, Fausset, Brown

Quoted verses:
1 Timothy 4:14 [see lesson]
Neglect not the gift that is in thee, which was given thee by prophecy, with the laying on of the hands of the presbytery.

2 Timothy 1:7 [see lesson]
For God hath not given us the spirit of fear; but of power, and of love, and of a sound mind.

3] Which is in thee by the putting on of my hands.

Most all the commentaries speaking to this phrase discuss Paul laying hands on Timothy, while considering 1 Timothy 4:14 [which we just read] and the act being carried out by others with Paul. Rather than spending time with this, we have remained focused on Salvation Process elements.