An examination is made of the conduction between sliding solids with heat energy generated along the region of contact. Based on a Green's function formulation, a Fredholm integral equation of the first kind is derived and an asymptotic solution for the heat flux partition to each solid is obtained for large Peclet numbers. By introducing further asymptotic approximations, closed-form expressions are derived for the temperature fields in the solids. Comparison with a numerical solution indicates that the asymptotic solutions are valid for Peclet numbers greater than ten, which covers most cases of practical interest. In addition, an examination of the present solution reveals the inadequacy of the empirical relations deduced by earlier workers for the estimation of the thermal penetration into the solids. An appropriate parameter for this correlation is suggested.