A device serves for controlling temperature of an optical element provided in vacuum atmosphere. The device has a cooling apparatus having a radiational cooling part, arranged apart from the optical element, for cooling the optical element by radiation heat transfer. A controller serves for controlling temperature of the radiational cooling part. Further, the device comprises a heating part for heating the optical element. The heating part is connected to the controller for controlling the temperature of the heating part. The resulting device for controlling temperature in particular can be used with an optical element in a EUV microlithography tool leading to a stable performance of its optics.