Objection 1. It would seem that Christ is not, as man, the Mediator of God and men. For Augustine says (Contra Felic. x): "One is the Person of Christ: lest there be not one Christ, not one substance; lest, the office of Mediator being denied, He be called the Son either of God alone, or merely the Son of a man." But He is the Son of God and man, not as man, but as at the same time God and man. Therefore neither should we say that, as man alone, He is Mediator of God and man.
Objection 2. Further, just as Christ, as God, has a common nature with the Father and the Holy Ghost; so, as man, He has a common nature with men. But for the reason that, as God, He has the same nature as the Father and the Holy Ghost, He cannot be called Mediator, as God: for on 1 Timothy 2:5, "Mediator of God and man," a gloss says: "As the Word, He is not a Mediator, because He is equal to God, and God 'with God,' and at the same time one God." Therefore neither, as man, can He be called Mediator, on account of His having the same nature as men.
Objection 3. Further, Christ is called Mediator, inasmuch as He reconciled us to God: and this He did by taking away sin, which separated us from God. But to take away sin belongs to Christ, not as man, but as God. Therefore Christ is our Mediator, not as man, but as God.
On the contrary, Augustine says (De Civ. Dei ix, 15): "Not because He is the Word, is Christ Mediator, since He Who is supremely immortal and supremely happy is far from us unhappy mortals; but He is Mediator, as man."
I answer that, We may consider two things in a mediator: first, that he is a mean; secondly, that he unites others. Now it is of the nature of a mean to be distant from each extreme: while it unites by communicating to one that which belongs to the other. Now neither of these can be applied to Christ as God, but only as man. For, as God, He does not differ from the Father and the Holy Ghost in nature and power of dominion: nor have the Father and the Holy Ghost anything that the Son has not, so that He be able to communicate to others something belonging to the Father or the Holy Ghost, as though it were belonging to others than Himself. But both can be applied to Him as man. Because, as man, He is distant both from God, by nature, and from man by dignity of both grace and glory. Again, it belongs to Him, as man, to unite men to God, by communicating to men both precepts and gifts, and by offering satisfaction and prayers to God for men. And therefore He is most truly called Mediator, as man.
Reply to Objection 1. If we take the Divine Nature from Christ, we consequently take from Him the singular fulness of grace, which belongs to Him as the Only-begotten of the Father, as it is written (John 1:14). From which fulness it resulted that He was established over all men, and approached nearer to God.
Reply to Objection 2. Christ, as God, is in all things equal to the Father. But even in the human nature He is above all men. Therefore, as man, He can be Mediator, but not as God.
Reply to Objection 3. Although it belongs to Christ as God to take away sin authoritatively, yet it belongs to Him, as man, to satisfy for the sin of the human race. And in this sense He is called the Mediator of God and men.
Source: Summa Theologica (New Advent)