The two-dimensional thermoelastic sliding frictional contact of the functionally graded materials (FGMs) coated half-plane under plain strain-state deformation is investigated in this paper. A rigid cylindrical punch is sliding over the surface of the FGM coating with the constant velocity, which is small compared with the Rayleigh wave velocity of the medium. Frictional heating is generated at the interface between the punch and FGM coating with its value proportional to contact pressure, friction coefficient and sliding velocity. The material properties of the coating change exponentially along the thickness direction. It is assumed that the area outside the contact region is both thermally insulated and traction-free. The Fourier integral transform method is employed to convert the problem into the Cauchy singular integral equations, which is then solved numerically to obtain the unknown contact pressure and the in-plane component of the surface stress. The effects of the gradient index, Peclet number, and friction coefficient on the thermoelastic contact characteristics are discussed in detail. Numerical results show that the change of the gradient index, Peclet number and friction coefficient can influence the distributions of the surface contact stress.