Abstract: The apparatus comprises a work surface heated by a heat carrier medium and located upon a heat-conducting layer carried by a metallic base body. The base body is provided with grooves at its surface confronting the heat-conducting layer and/or this heat-conducting layer is provided at its surface confronting the base body with grooves. The work surface is heated by infeeding the heat carrier medium into the grooves. To influence heat transfer to the heat-conducting layer carrying the work surface, particularly to a sheet metal plating or the like, for instance a cylinder jacket seated in direct metallic contact or only through the intermediate disposition of a transition layer of good thermal conductivity, upon the base body, there are provided control means regulating heat conduction from the base body to the heat-conducting layer and/or from the heat carrier medium guided in the grooves to the base body or the heat-conducting layer.