Abstract: A mirror system comprises an EUV mirror. The EUV mirror comprises a mirror body and an optical surface with high EUV radiation reflectivity. The mirror system further comprises a frame structure which carries the mirror body, a fluid channel for a temperature control fluid, the fluid channel extending in a structure body of the mirror system, and a feed line for supplying the temperature control fluid to the fluid channel. The feed line has a temperature sensor for the temperature control fluid temperature. The temperature sensor is arranged outside of the cross section of the feed line. A method for operating a mirror system and a projection lens of a microlithography projection exposure apparatus are disclosed.