According to the Catholic Dictionary:
In theological language, this penance is called satisfaction and is defined, in the words of St. Thomas: “The payment of the temporal punishment due on account of the offence committed against God by sin” (Suppl. to Summa, Q. xii, a. 3). It is an act of justice whereby the injury done to the honour of God is required, so far at least as the sinner is able to make reparation (poena vindicativa) ; it is also a preventive remedy, inasmuch as it is meant to hinder the further commission of sin (poena medicinalis). Satisfaction is not, like contrition and confession, an essential part of the sacrament, because the primary effect, i.e., remission of guilt and eternal punishment – is obtained without satisfaction; but it is an integral part, because it is requisite for obtaining the secondary effect – i.e., remission of the temporal punishment. The Catholic doctrine on this point is set forth by the Council of Trent, which condemns the proposition: “That the entire punishment is always remitted by God together with the guilt, and the satisfaction required of penitents is no other than faith whereby they believe that Christ has satisfied for them”; and further the proposition: “That the keys were given to the Church for loosing only and not for binding as well; that therefore in enjoining penance on those who confess, priests act contrary to the purpose of the keys and the institution of Christ; that it is a fiction [to say] that after the eternal punishment has been remitted in virtue of the keys, there usually remains to be paid a temporal penalty” (Can. “de Sac. poenit.”, 12, 15; Denzinger, “Enchir.”, 922, 925).
Note it reading this that those statements at the end are declared as false by the Council of Trent…don’t be confused and read them as true statements. In summary, this is saying that satisfaction (the carrying out of your penance) does have an effect to remit temporal punishment due from your sins. However, it does not specify if this is a partial or complete remission. In keeping with most of what I have read, I would say that the penance after confession grants a partial remission of the temporal punishment due.
