Objection 1. It would seem that consent belongs only to the apprehensive part of the soul. For Augustine (De Trin. xii, 12) ascribes consent to the higher reason. But the reason is an apprehensive power. Therefore consent belongs to an apprehensive power.
Objection 2. Further, consent is "co-sense." But sense is an apprehensive power. Therefore consent is the act of an apprehensive power.
Objection 3. Further, just as assent is an application of the intellect to something, so is consent. But assent belongs to the intellect, which is an apprehensive power. Therefore consent also belongs to an apprehensive power.
On the contrary, Damascene says (De Fide Orth. ii, 22) that "if a man judge without affection for that of which he judges, there is no sentence," i.e. consent. But affection belongs to the appetitive power. Therefore consent does also.
I answer that, Consent implies application of sense to something. Now it is proper to sense to take cognizance of things present; for the imagination apprehends the similitude of corporeal things, even in the absence of the things of which they bear the likeness; while the intellect apprehends universal ideas, which it can apprehend indifferently, whether the singulars be present or absent. And since the act of an appetitive power is a kind of inclination to the thing itself, the application of the appetitive power to the thing, in so far as it cleaves to it, gets by a kind of similitude, the name of sense, since, as it were, it acquires direct knowledge of the thing to which it cleaves, in so far as it takes complacency in it. Hence it is written (Wisdom 1:1): "Think of [Sentite] the Lord in goodness." And on these grounds consent is an act of the appetitive power.
Reply to Objection 1. As stated in De Anima iii, 9, "the will is in the reason." Hence, when Augustine ascribes consent to the reason, he takes reason as including the will.
Reply to Objection 2. Sense, properly speaking, belongs to the apprehensive faculty; but by way of similitude, in so far as it implies seeking acquaintance, it belongs to the appetitive power, as stated above.
Reply to Objection 3. "Assentire" [to assent] is, to speak, "ad aliud sentire" [to feel towards something]; and thus it implies a certain distance from that to which assent is given. But "consentire" [to consent] is "to feel with," and this implies a certain union to the object of consent. Hence the will, to which it belongs to tend to the thing itself, is more properly said to consent: whereas the intellect, whose act does not consist in a movement towards the thing, but rather the reverse, as we have stated in the I, 16, 01; I, 27, 4; I, 59, 2, is more properly said to assent: although one word is wont to be used for the other [In Latin rather than in English.]. We may also say that the intellect assents, in so far as it is moved by the will.
Source: Summa Theologica (New Advent)