A variation of the boundary element method is developed to determine the distribution of frictional heat and the ensuing surface or subsurface temperature rise caused by frictional heating between sliding solids. The theoretical model consists of two semi-infinite substrates each coated with a film of arbitrary thickness and thermal properties. A three dimensional transient analysis is developed which involves the thermal coupling of the two sliding solids at the true contact areas. The boundary element solution is based on a moving Green's function which naturally incorporates the combined conduction and convection effects due to sliding. Results are presented to display some of the important numerical characteristics of the boundary element solution method. Results are also presented that show the sensitivity of surface temperature rise to contact area evolvement, geometry and subdivision. The effects of surface film thickness and thermal properties on surface temperature rise are presented for a range of Peelet numbers. Lastly, a comparison of theoretical predictions and experimental measurements for surface temperature rise of a graphite epoxy ball loaded against a rotating sapphire disk is presented. / Master of Science