The integral equation approach of Klitsner and co-workers for boundary limited thermal conductance is adapted for calculating the surface temperature profile of wide slabshaped samples in which the temperature is independent of the large dimension transverse to the direction of heat flow. It is used to model the surface temperature of a silicon water in which a hot ?DEG is embedded. Noteworthy features emerging from this simulation are temperature discontinuities at the edges of the heat source and sink with the temperature gradient nearby being non-uniform, marked differences between the temperature profiles of the opposite faces, and the existence of a finite thermal gradient in regions where there is no net heat flux.