An explosion-proof apparatus with an explosion-proof housing and a cooling device. The explosion-proof housing has a plurality of outer walls enclosing a housing interior. A pressure-relief arrangement of the cooling device has at least one pressure relief opening with at least one gas-permeable, flameproof pressure-relief body. The pressure-relief opening passes through at least one of the outer walls. The cooling device also has at least one heat sink which forms at least one heat sink wall part of one the outer walls and which, as a heat sink wall part of this outer wall, directly borders, on its outer face, the surrounding area and directly borders, on its inner face, the housing interior.