||The steady-state temperature rise due to frictional heating on the surface of coated halfspaces and halfplanes is described by closed form expressions in the Fourier transformed frequency domain. These frequency response functions (FRFs) include the effects of the coating and the speed of the moving heat source and apply for all Peclet number regimes. Analytical inversion of these expressions for several special cases shows the Green's functions as infinite series of images, which may be costly and slowly convergent. Also, the influence coefficients integrated from these Green's functions are not available in closed form. Applying fast Fourier transform (FFT) methods to invert the frequency domain expressions does not rely on the infinite summations, and the influence coefficients can be computed quickly and accurately. The accuracy for several FFT methods are analyzed in comparison with available homogeneous cases (halfspace: low Peclet and high Peclet number approximations; halfplane: all Peclet numbers, as well as low and high Peclet number approximations). Finally, a brief parameter study about the effect of the coating is performed, using the discrete convolution fast Fourier transform (DC-FFT) algorithm for accurate and efficient calculations of the temperature rise from the frequency response functions.