For an engineering calculation of the maximum value of the mean surface temperature of a friction assembly, such as a brake or clutch, simple analytical and graphical relationships have been derived. A reduction of this temperature can be achieved by an increase of the thickness of backup block, by choosing material with as great a coefficient of thermal saturation as possible, and also by an increase of the slipping time, if this is permissible by the operational conditions of the machine. Cooling of the backup block during the friction process has practically no substantial effect on the mean surface temperature.