There has been a gradual increase in the field of parts recovery from cars that are withdrawn from use. However, the disposal of automotive shredder residue (ASR) still remains a significant problem. ASR is refuse derived fuel (RDF), which contains mainly plastics, fiber sponges, and rubbers in different proportions, and therefore a thermal treatment of selected waste samples is applied. The presented research includes thermogravimetry (TG) analysis and differential thermogravimetric (DTG) analysis, as well as a proximate and an ultimate analysis of the ASR samples. The obtained results were processed and used as an input for modelling. The numerical calculations focused on the identification of the ASR’s average composition, the raw pyrolysis process product, its dry pyrolytic gas composition, and the combustible properties of the pyrolytic gases. The TGA analysis with three heating rate levels covered the temperature range from ambient to 800 °C. The thermal decomposition of the studied samples was in three stages confirmed with three peaks observed at the temperatures 280, 470, and 670 °C. The amount of solid residue grew with the heating rates and was in the range of 27–32 wt%. The numerical calculation of the pyrolysis process showed that only 0.46 kg of dry gas were formed from 1 kg of ASR. The gas yield increased with the rising temperature, and, at the same time, its calorific value decreased from 19.22 down to 14.16 MJ/m3. This is due to the decomposition of C6+ hydrocarbons and the promotion of CO formation. The thermodynamic parameters of the combustion process for a pyrolytic gas air mixture, such as the adiabatic flame temperature and laminar flame speed, were higher than for methane and were, respectively, 2073 °C and 1.02 m/s.