How does the sacrament of penance relate to the idea of purgatory?

In Roman Catholic theology, the sacrament of penance and the concept of purgatory are deeply interconnected through the belief that forgiveness of sin involves both the removal of guilt and the satisfaction of temporal punishment.12

While the sacrament provides absolution for the guilt (culpa) of sin, Catholic tradition holds that the penitent must still undergo temporal punishment (poena) to address the offense against God. This satisfaction can be completed during one's lifetime through good works, such as prayer, almsgiving, or other acts of penance. However, if this debt of temporal punishment remains incomplete at the time of death, it must be satisfied in purgatory, a state of purification.1342

This framework also gave rise to the practice of indulgences, which are intended to remit some or all of this remaining temporal punishment. By drawing upon the "treasury of merits"—the infinite merits of Christ and the saints—the Church offers a means for the living to help themselves or the souls in purgatory reduce their remaining debt of sin.12