Analysis of a healed punch moving over the surface of a thermoelastic half-space is carried out for temperature and stress distribution in the medium. The formulation results in a mixed boundary-value problem independent of time in a moving nondimensional coordinate system. Exponential Fourier transforms are applied and the resulting system solved to obtain a general solution in terms of the functions expressed in the form of inverse Fourier transforms. Specifically, closed-form solutions are obtained for flat, cylindrical, and wedge punches. For a uniform temperature distribution the results derived agree with those available in the literature. Also, in the case of a concentrated force moving on the surface of an elastic half-space the solution obtained agrees with that in the literature.