The invention relates to an apparatus and method for exposing a sample. The apparatus comprises a source for electromagnetic radiation or particles having energy, an exposing unit for exposing said sample to said electromagnetic radiation or particles, and a substrate holding device for holding said sample at least during said exposing.The exposing unit comprises a component for manipulating and/or blocking at least part of the electromagnetic radiation or charged particles. The component comprises a cooling arrangement which is arranged for substantially maintaining the component at a predetermined first temperature.The substrate holding device comprises a temperature stabilizing arrangement which is arranged to substantially stabilize the temperature of a sample arranged on said substrate holding device. The temperature stabilizing arrangement comprises a phase change material having a phase change at a second temperature, which is at or near the first temperature.