Thomas Aquinas, Compendium of Theology

Although some souls may be admitted to eternal beatitude as soon as they are released from their bodies, others may be held back from this happiness for a time. For it sometimes happens that during their lives people have not done full penance for the sins they have committed, but for which they have been sorry in the end. Since the order of divine justice demands that punishment be undergone for sins, we must hold that souls pay after this life the penalty they have not paid while on earth. This does not mean that they are banished to the ultimate misery of the damned, since by their repentance they have been brought back to the state of charity, whereby they cleave to God as their last end, so that they have merited eternal life. Hence we conclude that there are certain purgatorial punishments after this life, by which the debt of penalty not previously paid is discharged.