Who are punished in purgatory? Those are punished for a time in purgatory who die in the state of grace but are guilty of venial sin, or have not fully satisfied for the temporal punishment due to their sins.
The fire will assay the quality of everyone's work; if his work abides which he has built thereon, he will receive reward; if his work burns he will lose his reward, but himself will be saved, yet so as through fire. (I Corinthians 3:13-15)