An optical arrangement in an optical system, such as a microlithographic projection exposure apparatus, includes: at least one heat-emitting subsystem which emits heat during the operation of the optical system; a first heat shield which is arranged such that it at least partly absorbs the heat emitted by the heat-emitting subsystem; a first cooling device which is in mechanical contact with the first heat shield and is designed to dissipate heat from the first heat shield; and a second heat shield which at least partly absorbs heat emitted by the first heat shield. The second heat shield is in mechanical contact with a cooling device that dissipates heat from the second heat shield.