Formal transport theory for heat conduction requires a constant thermal gradient over a small but finite distance ifQ=−KdT/dxis to be a good approximation. The kinetic model is used to show that this relation holds within 2% if the gradient is constant over a minimum range of ±5&Lgr;, where &Lgr; is the mean free path of electrons in metals. The usual differential equation of heat conduction cannot be applied to the absorption of blackbody radiation by metals if the absorption coefficient is high, since it overestimates the effect of thermal conduction and does not give the correct temperature distribution within the first few mean free paths from the surface.