Problem. The mathematical description of the temperature field of the rim of the brake pulley can have both an independent value and be the goal of solving a problem (for example, when calculating the time of heating or forced cooling), and also be used as an auxiliary result for solving another, more complex problem (for example, calculating thermoelastic stresses in brake pulley rim). Goal. The purpose of the work is to assess the energy load of metal friction brake elements during the braking process. Methodology. Solving the tasks involved taking into account the fact that the surface-volume temperatures of the polished working surface of the pulley rim are local when assessing the energy load of the belt pulley rim; surface-volume temperatures are always higher than the "pure" volume temperatures of the pulley rim; polished and matte surfaces of the pulley rim are considered. Results. It is proposed that a new approach to the calculation of local thermal stresses, which is implemented for the first time in the theory of friction and wear. The reliability of the obtained results was confirmed experimentally. Originality. The need to find the non-stationary field in the investigated single- ("pad-pulley") and in multi-pair ("tape-pad" and "pad-pulley") friction nodes is proposed. In the last friction nodes, the friction pads act as insulation between the tape, which is freed from the pads, and the working surface of the brake pulley rim. Practical value. The proposed approach made it possible to establish that the magnitude of stresses on the surface of heat release is almost 5 times greater than in the volume of the pulley rim. At the same time, the nature of the influence of the intensity of heat exchange on the magnitude of stresses is the same as during heating, which leads to a decrease in the formation of cracks on the surface of the pulley rim.