Objection 1. It would seem that in Christ there was the "fomes" of sin. For the "fomes" of sin, and the passibility and mortality of the body spring from the same principle, to wit, from the withdrawal of original justice, whereby the inferior powers of the soul were subject to the reason, and the body to the soul. Now passibility and mortality of body were in Christ. Therefore there was also the "fomes" of sin.
Objection 2. Further, as Damascene says (De Fide Orth. iii, 19), "it was by consent of the Divine will that the flesh of Christ was allowed to suffer and do what belonged to it." But it is proper to the flesh to lust after its pleasures. Now since the "fomes" of sin is nothing more than concupiscence, as the gloss says on Romans 7:8, it seems that in Christ there was the "fomes" of sin.
Objection 3. Further, it is by reason of the "fomes" of sin that "the flesh lusteth against the spirit," as is written (Galatians 5:17). But the spirit is shown to be so much the stronger and worthier to be crowned according as the more completely it overcomes its enemy--to wit, the concupiscence of the flesh, according to 2 Timothy 2:5, he "is not crowned except he strive lawfully." Now Christ had a most valiant and conquering spirit, and one most worthy of a crown, according to Apocalypse 6:2: "There was a crown given Him, and He went forth conquering that He might conquer." Therefore it would especially seem that the "fomes" of sin ought to have been in Christ.
On the contrary, It is written (Matthew 1:20): "That which is conceived in her is of the Holy Ghost." Now the Holy Ghost drives out sin and the inclination to sin, which is implied in the word "fomes." Therefore in Christ there ought not to have been the "fomes" of sin.
I answer that, As was said above (7, 2,9), Christ had grace and all the virtues most perfectly. Now moral virtues, which are in the irrational part of the soul, make it subject to reason, and so much the more as the virtue is more perfect; thus, temperance controls the concupiscible appetite, fortitude and meekness the irascible appetite, as was said in I-II, 56, 4. But there belongs to the very nature of the "fomes" of sin an inclination of the sensual appetite to what is contrary to reason. And hence it is plain that the more perfect the virtues are in any man, the weaker the "fomes" of sin becomes in him. Hence, since in Christ the virtues were in their highest degree, the "fomes" of sin was nowise in Him; inasmuch, also, as this defect cannot be ordained to satisfaction, but rather inclined to what is contrary to satisfaction.
Reply to Objection 1. The inferior powers pertaining to the sensitive appetite have a natural capacity to be obedient to reason; but not the bodily powers, nor those of the bodily humors, nor those of the vegetative soul, as is made plain Ethic. i, 13. And hence perfection of virtue, which is in accordance with right reason, does not exclude passibility of body; yet it excludes the "fomes" of sin, the nature of which consists in the resistance of the sensitive appetite to reason.
Reply to Objection 2. The flesh naturally seeks what is pleasing to it by the concupiscence of the sensitive appetite; but the flesh of man, who is a rational animal, seeks this after the manner and order of reason. And thus with the concupiscence of the sensitive appetite Christ's flesh naturally sought food, drink, and sleep, and all else that is sought in right reason, as is plain from Damascene (De Fide Orth. iii, 14). Yet it does not therefore follow that in Christ there was the "fomes" of sin, for this implies the lust after pleasurable things against the order of reason.
Reply to Objection 3. The spirit gives evidence of fortitude to some extent by resisting that concupiscence of the flesh which is opposed to it; yet a greater fortitude of spirit is shown, if by its strength the flesh is thoroughly overcome, so as to be incapable of lusting against the spirit. And hence this belonged to Christ, whose spirit reached the highest degree of fortitude. And although He suffered no internal assault on the part of the "fomes" of sin, He sustained an external assault on the part of the world and the devil, and won the crown of victory by overcoming them.
Source: Summa Theologica (New Advent)