In this paper, based on the theoretical analysis of steady-state heat conduction and a plastic limit state, the analytical expressions are presented for both the steady-state temperature fields and thermal elastic-plastic stresses in cylinders of ceramic/metal functionally graded materials (FGM) through the thickness of the cylinder. Based on the theoretical analysis of the limit state defined in this paper, the optimal design for the parameters of the FGM design is carried out. Analytical solutions of the steady-state temperature field and thermal elastic-plastic stresses are discussed for the ZrO2/Ti-6Al-4V system.