Stratification due to ion-ion friction in a magnetized multiple-ion species plasma is shown to be accompanied by a heat pump effect, identified for the first time here, transferring heat from one ion species to another as well as from one region of space to another. The heat pump is produced via newly identified heating mechanisms associated with charge incompressibility and the Ettingshausen effect. Besides their academic interest, these new effects may have useful applications to plasma technologies that involve rotation or compression.