Abstract: For tempering by contact of a glass sheet having a through hole, cooled clamping pieces coated with thermoresistant fibers having a high thermal conductivity act on the surfaces of the glass sheet heated to the tempering temperature. During the action of the clamping plates, the inner surfaces of the glass sheet defining the hole are struck by a cooling gas. The cooling gas is injected by a jet or nozzle tube located in a clamping plate within a bore, which passes coaxially through the air-permeable covering fabric and, after having been whirled up within the hole, escapes through the fabric via a backflow pipe surrounding the jet or nozzle tube.