This paper investigates the frictionally excited thermoelastic instability (TEI) of a functionally graded material (FGM) half-plane sliding against a homogeneous half-plane at the out-of-plane direction with the thermal contact resistance. A uniform pressure presses these two half-planes together. The material properties of FGMs are assumed to be varied as an exponential form. Using the perturbation method, we derive the characteristic equation for the TEI problem to solve the unknown critical heat flux and critical sliding speed. The effects of the thermal contact resistance, gradient index, friction coefficient, and heat generation factor on the stability boundaries are discussed for four different material combinations. The results may provide a possible method to improve the contact stability in the sliding system by using FGMs.