||Computing the temperature rise and thermoelastic displacement of a material subjected to frictional heating is essential for the realistic modeling of the performance of mechanical components. This paper presents a novel set of frequency-domain expressions for the surface temperature rise and the surface normal thermoelastic displacement of a moving three-dimensional elastic halfspace subjected to arbitrary transient frictional heating, where the velocity of the body and its direction can be an arbitrary function of time. Frequency response functions are derived by using the Carslaw-Jaeger theory, the Seo-Mura result, and the Fourier transform. General formulas are expressed in the form of time integrals, and important expressions for constant body motion velocities are given for the transient-instantaneous, transient-continuous, and steady-state cases. The thermoelastic responses, in terms of temperature rise and thermoelastic displacement, of the halfspace surface in configurations similar to pin-on-disk contacts are simulated and discussed.