Objection 1. It would seem that it was not becoming for Christ to be tempted. For to tempt is to make an experiment, which is not done save in regard to something unknown. But the power of Christ was known even to the demons; for it is written (Luke 4:41) that "He suffered them not to speak, for they knew that He was Christ." Therefore it seems that it was unbecoming for Christ to be tempted.
Objection 2. Further, Christ was come in order to destroy the works of the devil, according to 1 John 3:8: "For this purpose the Son of God appeared, that He might destroy the works of the devil." But it is not for the same to destroy the works of a certain one and to suffer them. Therefore it seems unbecoming that Christ should suffer Himself to be tempted by the devil.
Objection 3. Further, temptation is from a threefold source--the flesh, the world, and the devil. But Christ was not tempted either by the flesh or by the world. Therefore neither should He have been tempted by the devil.
On the contrary, It is written (Matthew 4:1): "Jesus was led by the Spirit into the desert to be tempted by the devil."
I answer that, Christ wished to be tempted; first that He might strengthen us against temptations. Hence Gregory says in a homily (xvi in Evang.): "It was not unworthy of our Redeemer to wish to be tempted, who came also to be slain; in order that by His temptations He might conquer our temptations, just as by His death He overcame our death."
Secondly, that we might be warned, so that none, however holy, may think himself safe or free from temptation. Wherefore also He wished to be tempted after His baptism, because, as Hilary says (Super Matth., cap. iii.): "The temptations of the devil assail those principally who are sanctified, for he desires, above all, to overcome the holy. Hence also it is written (Sirach 2): Son, when thou comest to the service of God, stand in justice and in fear, and prepare thy soul for temptation."
Thirdly, in order to give us an example: to teach us, to wit, how to overcome the temptations of the devil. Hence Augustine says (De Trin. iv) that Christ "allowed Himself to be tempted" by the devil, "that He might be our Mediator in overcoming temptations, not only by helping us, but also by giving us an example."
Fourthly, in order to fill us with confidence in His mercy. Hence it is written (Hebrews 4:15): "We have not a high-priest, who cannot have compassion on our infirmities, but one tempted in all things like as we are, without sin."
Reply to Objection 1. As Augustine says (De Civ. Dei ix): "Christ was known to the demons only so far as He willed; not as the Author of eternal life, but as the cause of certain temporal effects," from which they formed a certain conjecture that Christ was the Son of God. But since they also observed in Him certain signs of human frailty, they did not know for certain that He was the Son of God: wherefore (the devil) wished to tempt Him. This is implied by the words of Matthew 4:2-3, saying that, after "He was hungry, the tempter" came "to Him," because, as Hilary says (Super Matth., cap. iii), "Had not Christ's weakness in hungering betrayed His human nature, the devil would not have dared to tempt Him." Moreover, this appears from the very manner of the temptation, when he said: "If Thou be the Son of God." Which words Ambrose explains as follows (In Luc. iv): "What means this way of addressing Him, save that, though he knew that the Son of God was to come, yet he did not think that He had come in the weakness of the flesh?"
Reply to Objection 2. Christ came to destroy the works of the devil, not by powerful deeds, but rather by suffering from him and his members, so as to conquer the devil by righteousness, not by power; thus Augustine says (De Trin. xiii) that "the devil was to be overcome, not by the power of God, but by righteousness." And therefore in regard to Christ's temptation we must consider what He did of His own will and what He suffered from the devil. For that He allowed Himself to be tempted was due to His own will. Wherefore it is written (Matthew 4:1): "Jesus was led by the Spirit into the desert, to be tempted by the devil"; and Gregory (Hom. xvi in Evang.) says this is to be understood of the Holy Ghost, to wit, that "thither did His Spirit lead Him, where the wicked spirit would find Him and tempt Him." But He suffered from the devil in being "taken up" on to "the pinnacle of the Temple" and again "into a very high mountain." Nor is it strange, as Gregory observes, "that He allowed Himself to be taken by him on to a mountain, who allowed Himself to be crucified by His members." And we understand Him to have been taken up by the devil, not, as it were, by force, but because, as Origen says (Hom. xxi super Luc.), "He followed Him in the course of His temptation like a wrestler advancing of his own accord."
Reply to Objection 3. As the Apostle says (Hebrews 4:15), Christ wished to be "tempted in all things, without sin." Now temptation which comes from an enemy can be without sin: because it comes about by merely outward suggestion. But temptation which comes from the flesh cannot be without sin, because such a temptation is caused by pleasure and concupiscence; and, as Augustine says (De Civ. Dei xix), "it is not without sin that 'the flesh desireth against the spirit.'" And hence Christ wished to be tempted by an enemy, but not by the flesh.
Source: Summa Theologica (New Advent)