Objection 1. It would seem that a priest cannot remit sin as to the punishment. For sin deserves eternal and temporal punishment. But after the priest's absolution the penitent is still obliged to undergo temporal punishment either in Purgatory or in this world. Therefore the priest does not remit the punishment in any way.
Objection 2. Further, the priest cannot anticipate the judgment of God. But Divine justice appoints the punishment which penitents have to undergo. Therefore the priest cannot remit any part of it.
Objection 3. Further, a man who has committed a slight sin, is not less susceptible to the power of the keys, than one who has committed a graver sin. Now if the punishment for the graver sin be lessened in any way through the priestly administrations, it would be possible for a sin to be so slight that the punishment which it deserves is no greater than that which has been remitted for the graver sin. Therefore the priest would be able to remit the entire punishment due for the slight sin: which is false.
Objection 4. Further, the whole of the temporal punishment due for a sin is of one kind. If, therefore, by a first absolution something is taken away from the punishment, it will be possible for something more to be taken away by a second absolution, so that the absolution can be so often repeated, that by virtue of the keys the whole punishment will be taken away, since the second absolution is not less efficacious than the first: and consequently that sin will be altogether unpunished, which is absurd.
On the contrary, The key is the power of binding and loosing. But the priest can enjoin a temporal punishment. Therefore he can absolve from punishment.
Further, the priest cannot remit sin either as to the guilt [St. Thomas here follows the opinion of Peter Lombard, and replies in the negative. Later in life he altered his opinion. Cf. III, 62, 1; III, 64, 1; III, 86, 6], as stated in the text (Sent. iv, D, 18), or as to the eternal punishment, for a like reason. If therefore he cannot remit sin as to the temporal punishment, he would be unable to remit sin in any way, which is altogether contrary to the words of the Gospel.
I answer that, Whatever may be said of the effect of Baptism conferred on one who has already received grace, applies equally to the effect of the actual exercise of the power of the keys on one who has already been contrite. For a man may obtain the grace of the remission of his sins as to their guilt, through faith and contrition, previous to Baptism; but when, afterwards, he actually receives Baptism, his grace is increased, and he is entirely absolved from the debt of punishment, since he is then made a partaker of the Passion of Christ. In like manner when a man, through contrition, has received the pardon of his sins as to their guilt, and consequently as to the debt of eternal punishment, (which is remitted together with the guilt) by virtue of the keys which derive their efficacy from the Passion of Christ, his grace is increased and the temporal punishment is remitted, the debt of which remained after the guilt had been forgiven. However, this temporal punishment is not entirely remitted, as in Baptism, but only partly, because the man who is regenerated in Baptism is conformed to the Passion of Christ, by receiving into himself entirely the efficacy of Christ's Passion, which suffices for the blotting out of all punishment, so that nothing remains of the punishment due to his preceding actual sins. For nothing should be imputed to a man unto punishment, save what he has done himself, and in Baptism man begins a new life, and by the baptismal water becomes a new man, as that no debt for previous sin remains in him. on the other hand, in Penance, a man does not take on a new life, since therein he is not born again, but healed. Consequently by virtue of the keys which produce their effect in the sacrament of Penance, the punishment is not entirely remitted, but something is taken off the temporal punishment, the debt of which could remain after the eternal punishment had been remitted. Nor does this apply only to the temporal punishment which the penitent owes at the time of confession, as some hold, (for then confession and sacramental absolution would be mere burdens, which cannot be said of the sacraments of the New Law), but also to the punishment due in Purgatory, so that one who has been absolved and dies before making satisfaction, is less punished in Purgatory, than if he had died before receiving absolution.
Reply to Objection 1. The priest does not remit the entire temporal punishment, but part of it; wherefore the penitent still remains obliged to undergo satisfactory punishment.
Reply to Objection 2. Christ's Passion was sufficiently satisfactory for the sins of the whole world, so that without prejudice to Divine justice something can be remitted from the punishment which a sinner deserves, in so far as the effect of Christ's Passion reaches him through the sacraments of the Church.
Reply to Objection 3. Some satisfactory punishment must remain for each sin, so as to provide a remedy against it. Wherefore though, by virtue of the absolution some measure of the punishment due to a grave sin is remitted, it does not follow that the same measure of punishment is remitted for each sin, because in that case some sin would remain without any punishment at all: but, by virtue of the keys, the punishments due to various sins are remitted in due proportion.
Reply to Objection 4. Some say that at the first absolution, as much as possible is remitted by virtue of the keys, and that, nevertheless, the second confession is valid, on account of the instruction received, on account of the additional surety, on account of the prayers of the priest or confessor, and lastly on account of the merit of the shame.
But this does not seem to be true, for though there might be a reason for repeating the confession, there would be no reason for repeating the absolution, especially if the penitent has no cause to doubt about his previous absolution; for he might just as well doubt after the second as after the first absolution: even as we see that the sacrament of Extreme Unction is not repeated during the same sickness, for the reason that all that could be done through the sacrament, has been done once. Moreover, in the second confession, there would be no need for the confessor to have the keys, if the power of the keys had no effect therein.
For these reasons others say that even in the second absolution something of the punishment is remitted by virtue of the keys, because when absolution is given a second time, grace is increased, and the greater the grace received, the less there remains of the blemish of the previous sin, and the less punishment is required to remove that blemish. Wherefore even when a man is first absolved, his punishment is more or less remitted by virtue of the keys, according as he disposes himself more or less to receive grace; and this disposition may be so great, that even by virtue of his contrition the whole punishment is remitted, as we have already stated (5, 2). Consequently it is not unreasonable, if by frequent confession even the whole punishment be remitted, that a sin remain altogether unpunished, since Christ made satisfaction for its punishment.
Source: Summa Theologica (New Advent)