An illumination system of a microlithographic projection exposure apparatus includes a primary light source, a system pupil surface and a mirror array. The mirror array is arranged between the primary light source and the system pupil surface. The mirror array includes a plurality of adaptive mirror elements. Each mirror element includes a mirror support and a reflective coating. Each mirror element is configured to direct light produced by the primary light source towards the system pupil surface. The mirror elements can be tiltably mounted with respect to a support structure. The mirror elements include structures having a different coefficient of thermal expansion and being fixedly attached to one another. A temperature control device is configured to variably modify the temperature distribution within the structures to change the shape of the mirror elements.