The dialysis device (2) has an inlet (4) for conveying a dialysis fluid to a dialysis membrane (8) in a flow direction (6) and an outlet (10) for discharging a dialysate from the dialysis membrane. A heat pump (12) is coupled with the inlet to exchange heat energy between a heat reservoir (14) and the dialysis fluid in the inlet. An independent claim is also included for a method for operating a dialysis device.