A temperature control apparatus for controlling the temperature, in particular for the drying, of objects, in particular vehicle bodies, having a housing, in which a cooling zone having a cooling chamber that defines a longitudinal direction is accommodated. The cooling chamber is assigned at least one cooling-air temperature control device, by means of which temperature-controlled cooling air can be produced, which can be fed to the cooling chamber. In the longitudinal direction, the cooling zone comprises a supply chamber on one longitudinal side of the cooling chamber, in which supply chamber the cooling-air temperature control device is arranged.