This paper consists of two parts. The first one contains a description and methodology of the composite material used as friction material in clutches. Four variants of such material, differing in the type of carbon additive (the elemental graphite, pencil graphite and foundry coke powder of various fractions) were considered. Thermal conductivity, thermal diffusivity as well as the specific heat all materials were determined experimentally. On the inertial IM-58 stand, a simulation of the braking process of the friction pair consisting of a steel disc with friction material and a counterpart in the form of a homogeneous steel disc was carried out. On this basis, averaged coefficients of friction, unchanging in the entire sliding process, were found for the four friction pairs. The experimental data obtained in the first stage were used in the second stage to develop two (2D and 3D) numerical models of the friction heating process of the friction pairs under consideration. For four variants of the friction material, a comparative spatial-temporal temperature analysis was performed using both models. It was found that a simplified axisymmetric (2D) model can be used to estimate the maximum temperature with high accuracy. The lowest maximum temperature (115.6 °C) obtained for the same total friction work was achieved on the friction surface of the material with the addition of GP-1.