Objection 1. It would seem that no debt of punishment remains after the guilt has been forgiven through Penance. For when the cause is removed, the effect is removed. But the guilt is the cause of the debt of punishment: since a man deserves to be punished because he has been guilty of a sin. Therefore when the sin has been forgiven, no debt of punishment can remain.
Objection 2. Further, according to the Apostle (Romans 5) the gift of Christ is more effective than the sin of Adam. Now, by sinning, man incurs at the same time guilt and the debt of punishment. Much more therefore, by the gift of grace, is the guilt forgiven and at the same time the debt of punishment remitted.
Objection 3. Further, the forgiveness of sins is effected in Penance through the power of Christ's Passion, according to Romans 3:25: "Whom God hath proposed to be a propitiation, through faith in His Blood... for the remission of former sins." Now Christ's Passion made satisfaction sufficient for all sins, as stated above (Q48,49,79, 5). Therefore after the guilt has been pardoned, no debt of punishment remains.
On the contrary, It is related (2 Samuel 12:13) that when David penitent had said to Nathan: "I have sinned against the Lord," Nathan said to him: "The Lord also hath taken away thy sin, thou shalt not die. Nevertheless... the child that is born to thee shall surely die," which was to punish him for the sin he had committed, as stated in the same place. Therefore a debt of some punishment remains after the guilt has been forgiven.
I answer that, As stated in I-II, 87, 4, in mortal sin there are two things, namely, a turning from the immutable Good, and an inordinate turning to mutable good. Accordingly, in so far as mortal sin turns away from the immutable Good, it induces a debt of eternal punishment, so that whosoever sins against the eternal Good should be punished eternally. Again, in so far as mortal sin turns inordinately to a mutable good, it gives rise to a debt of some punishment, because the disorder of guilt is not brought back to the order of justice, except by punishment: since it is just that he who has been too indulgent to his will, should suffer something against his will, for thus will equality be restored. Hence it is written (Apocalypse 18:7): "As much as she hath glorified herself, and lived in delicacies, so much torment and sorrow give ye to her."
Since, however, the turning to mutable good is finite, sin does not, in this respect, induce a debt of eternal punishment. Wherefore, if man turns inordinately to a mutable good, without turning from God, as happens in venial sins, he incurs a debt, not of eternal but of temporal punishment. Consequently when guilt is pardoned through grace, the soul ceases to be turned away from God, through being united to God by grace: so that at the same time, the debt of punishment is taken away, albeit a debt of some temporal punishment may yet remain.
Reply to Objection 1. Mortal sin both turns away from God and turns to a created good. But, as stated in I-II, 71, 6, the turning away from God is as its form while the turning to created good is as its matter. Now if the formal element of anything be removed, the species is taken away: thus, if you take away rational, you take away the human species. Consequently mortal sin is said to be pardoned from the very fact that, by means of grace, the aversion of the mind from God is taken away together with the debt of eternal punishment: and yet the material element remains, viz. the inordinate turning to a created good, for which a debt of temporal punishment is due.
Reply to Objection 2. As stated in I-II, 109, 7,8; I-II, 111, 2, it belongs to grace to operate in man by justifying him from sin, and to co-operate with man that his work may be rightly done. Consequently the forgiveness of guilt and of the debt of eternal punishment belongs to operating grace, while the remission of the debt of temporal punishment belongs to co-operating grace, in so far as man, by bearing punishment patiently with the help of Divine grace, is released also from the debt of temporal punishment. Consequently just as the effect of operating grace precedes the effect of co-operating grace, so too, the remission of guilt and of eternal punishment precedes the complete release from temporal punishment, since both are from grace, but the former, from grace alone, the latter, from grace and free-will.
Reply to Objection 3. Christ's Passion is of itself sufficient to remove all debt of punishment, not only eternal, but also temporal; and man is released from the debt of punishment according to the measure of his share in the power of Christ's Passion. Now in Baptism man shares the Power of Christ's Passion fully, since by water and the Spirit of Christ, he dies with Him to sin, and is born again in Him to a new life, so that, in Baptism, man receives the remission of all debt of punishment. In Penance, on the other hand, man shares in the power of Christ's Passion according to the measure of his own acts, which are the matter of Penance, as water is of Baptism, as stated above (84, 1,3). Wherefore the entire debt of punishment is not remitted at once after the first act of Penance, by which act the guilt is remitted, but only when all the acts of Penance have been completed.
Source: Summa Theologica (New Advent)