A method for producing a multilayer coating (17) for reflecting radiation in the soft X-ray or EUV wavelength range on an optical element (8, 9) operated at an operating temperature (TOP) of 30° C. or more, including: determining an optical design for the multilayer coating (17) which defines an optical desired layer thickness (nOP dOP) of the layers (17.1, 17.2) of the multilayer coating (17) at the operating temperature (TOP), and applying the layers (17.1, 17.2) of the multilayer coating (17) with an optical actual layer thickness (nB dB) chosen such that a layer thickness change(nOP dOP−nB dB) caused by thermal expansion of the layers (17.1, 17.2) between the coating temperature (TB) and the operating temperature (TOP) is compensated for. Also provided are an associated optical element (8, 9) and a projection exposure apparatus having at least one such optical element (8, 9).