A microlithographic projection exposure apparatus includes a projection lens that is configured for immersion operation. For this purpose an immersion liquid is introduced into an immersion space that is located between a last lens of the projection lens on the image side and a photosensitive layer to be exposed. To reduce fluctuations of refractive index resulting from temperature gradients occurring within the immersion liquid, the projection exposure apparatus includes heat transfer elements that heat or cool partial volumes of the immersion liquid so as to achieve an at least substantially homogenous or at least substantially rotationally symmetric temperature distribution within the immersion liquid.