Thermally stable composites obtained by the low-temperature carbonization of an elastomeric matrix filled with hard dispersed silicon carbide particles were obtained and investigated. Evolution of the microstructure and of mechanical and thermal characteristics of composites during thermal degradation and carbonization processes in a wide range of filling from 0 to 450 parts per hundred rubber was studied. For highly filled composites, the compressive strength values were found to be more than 200 MPa; Young’s modulus was more than 15 GPa. The thermal conductivity coefficient of composites was up to 1.6 W/(m·K), and this magnitude varied slightly in the temperature range of 25–300 °C. Coupled with the high thermal stability of the composites, the observed properties make it possible to consider using such composites as strained friction units instead of reinforced polymers.