In thermal print heads for high printing capacity, the residual heat which is not transmitted to the recording medium must be conducted away by the time the heating element is energised again. The invention provides a substrate (1) made of a highly heat-conductive material with a heat conductivity lambda which is greater than 140 (W/m.K). The thickness of the substrate (1) is dimensioned such that the heat to be conducted away is distributed over a wide area at the junction face between the substrate (1) and a heat sink (7). In order to improve the conductance of heat, a heat-conducting adhesive layer (6) or a heat-conducting film is arranged between the substrate (1) and the heat sink (7). <IMAGE>