A numerical model designed to simulate a moving line contact of two rough layered bodies is presented. Fourier transforms are used to obtain fundamental solutions to relevant differential equations and then these solutions are used as kernel functions in a numerical scheme designed to provide a full thermomechanical solution for real layered contacts. The model assumes steady state heat transfer and predicts contact pressures and deformations, contact temperature rise, and resulting thermal stresses. The heat division between the contacting components is fully accounted for, as are the interactions between the mechanical and thermal displacements. Some results are presented to illustrate the potential importance of a full thermomechanical analysis as compared to a purely mechanical one as well as to demonstrate the influence of coating properties and surface roughness structure on the contact temperatures.