Objection 1. It would seem that concupiscence is not only in the sensitive appetite. For there is a concupiscence of wisdom, according to Wisdom 6:21: "The concupiscence [Douay: 'desire'] of wisdom bringeth to the everlasting kingdom." But the sensitive appetite can have no tendency to wisdom. Therefore concupiscence is not only in the sensitive appetite.
Objection 2. Further, the desire for the commandments of God is not in the sensitive appetite: in fact the Apostle says (Romans 7:18): "There dwelleth not in me, that is to say, in my flesh, that which is good." But desire for God's commandments is an act of concupiscence, according to Psalm 118:20: "My soul hath coveted [concupivit] to long for thy justifications." Therefore concupiscence is not only in the sensitive appetite.
Objection 3. Further, to each power, its proper good is a matter of concupiscence. Therefore concupiscence is in each power of the soul, and not only in the sensitive appetite.
On the contrary, Damascene says (De Fide Orth. ii, 12) that "the irrational part which is subject and amenable to reason, is divided into the faculties of concupiscence and anger. This is the irrational part of the soul, passive and appetitive." Therefore concupiscence is in the sensitive appetite.
I answer that, As the Philosopher says (Rhet. i, 11), "concupiscence is a craving for that which is pleasant." Now pleasure is twofold, as we shall state later on (31, 3,4): one is in the intelligible good, which is the good of reason; the other is in good perceptible to the senses. The former pleasure seems to belong to soul alone: whereas the latter belongs to both soul and body: because the sense is a power seated in a bodily organ: wherefore sensible good is the good of the whole composite. Now concupiscence seems to be the craving for this latter pleasure, since it belongs to the united soul and body, as is implied by the Latin word "concupiscentia." Therefore, properly speaking, concupiscence is in the sensitive appetite, and in the concupiscible faculty, which takes its name from it.
Reply to Objection 1. The craving for wisdom, or other spiritual goods, is sometimes called concupiscence; either by reason of a certain likeness; or on account of the craving in the higher part of the soul being so vehement that it overflows into the lower appetite, so that the latter also, in its own way, tends to the spiritual good, following the lead of the higher appetite, the result being that the body itself renders its service in spiritual matters, according to Psalm 83:3: "My heart and my flesh have rejoiced in the living God."
Reply to Objection 2. Properly speaking, desire may be not only in the lower, but also in the higher appetite. For it does not imply fellowship in craving, as concupiscence does; but simply movement towards the thing desired.
Reply to Objection 3. It belongs to each power of the soul to seek its proper good by the natural appetite, which does not arise from apprehension. But the craving for good, by the animal appetite, which arises from apprehension, belongs to the appetitive power alone. And to crave a thing under the aspect of something delightful to the senses, wherein concupiscence properly consists, belongs to the concupiscible power.
Source: Summa Theologica (New Advent)