Abstract: An oxygenator with a housing wall, which delimits a housing space with a blood inlet and a blood outlet, a gas inlet and a gas outlet, has a heating element which is arranged in the oxygenator between blood inlet and blood outlet in order to control the temperature of blood flowing through the housing space. For this purpose, the oxygenator has a radiation source and a receiver. The radiation source can be an infrared emitter and the receiver a matte-black surface, or the radiation source is an induction coil and the receiver has a material capable of induction. In a method for regulating the heat output on a heating element of an oxygenator, the through-flow of the blood through the oxygenator and the power of a pump acting on the through-flow are measured, and the heating power is adjusted in accordance therewith.