The housing (2) has a housing wall with at least one air guide element (26,28) in an outer surface (30) of the housing wall for guiding air along the outer surface. The air guide element can be a web-like raised formation in the outer surface of the housing wall or a formation of the housing wall. The guide element forms the highest protrusion from the housing wall at least along most of its length. AN Independent claim is also included for the following: (a) a cooking device with an inventive housing.