The main task of the frictional facing of a clutch disc is to transfer the power from the driving to the driven parts. High frictional heat will be generated when the frictional facing comes into contact with the moving surfaces (flywheel and pressure plate). In this research paper, the selection of the frictional-facing material of the clutch disc has been investigated to obtain the optimal thermal behavior of the clutch system. It used five different frictional materials (St37-2, HCC, G95, LUK, and Tiger), and then applied the Weighted Factor Method to find the optimal frictional material that can be used in the clutch disc. In the second part, an axisymmetric finite element (FE) model has been developed to simulate the working of the clutch system during the heating phase. A comparison was made between the results of the thermal problem using the FE method and the Weighted Factor Method, where a high agreement was obtained between them to determine the optimal frictional material for the clutch disc. It was found that the frictional material (HCC) is the superior one with the highest performance index equal to 90.7 and the lowest values of the maximum temperature (353.7 K). In contrast, the frictional material (St37-2) is the poorest one, with the lowest performance index equal to 30.7 and the highest values of the maximum temperature (378.2 K).