Sliding electrical contacts are found in many electromechanical devices, such as relays, switches, and resistance spot welding. Temperature rise due to sliding friction and electrical current may be the major source of sliding electrical contact deterioration. This paper reports the development of a three-dimensional thermo-elasto-plastic contact model of counterformal bodies, which takes into account transient heat flux, temperature-dependent strain hardening behavior, and a realistic heat partition between surfaces. Transient contact simulations induce a significant increase in computational burden. The discrete convolution and fast Fourier transform and the conjugate gradient method are utilized to improve the computation efficiency. The present model is used to study the case of a half-space sliding over a stationary sphere, and both are made of 7075 aluminum alloy; the contact resistance is considered mainly due to the surface oxide film. The simulation results indicate that the transient contact model is able to capture the history of plastic deformation accumulation and the material melting inception.