High temperatures appear in the contacting surfaces of a single-disc clutch system (friction clutch disc, flywheel and pressure plate) due to the relative motion between these parts during the sliding period. These high temperatures are responsible for several disadvantages such as increasing wear rate, surface cracks and permanent distortions. In some cases, these disadvantages may lead the contacting surfaces to failure before the expected lifetime. In this work, mathematical models of the friction clutch system (single-disc clutch) were built to find the temperature field during the sliding period (single engagement). Analysis has been completed using developed axisymmetric models to simulate the friction clutch system during the engagement. The surface temperatures are found based on uniform pressure and uniform wear assumptions.