Steady-state heat conduction through an insulating layer separating the surface of a rough, isothermal body (e.g. a sphere) from an isothermal semi-infinite region bounded by a rough plane is modeled by employing Robin boundary conditions with a ’slip’ coefficient on the smoothed body surface and plane. This model is proposed for circumstances where the roughness asparities are comparable in size to the nominal gap width (and each asparity is much smaller than the characteristic body radius). It is shown that Such slip, however small, serves to remove the logarithmic gap-width singularity in the contact case. An attempt is made to rationalize use of this ’effective’ boundary condition of the third kind, as well as to obtain an estimate for the slip coefficient appearing therein in terms of the scale of the asparities relative to the gap width. In this first attempt to develop a theory, particular attention is paid to the elementary case where the body is spherical in shape.