Say you have a flat resistor that is producing heat. You place the resistor against a sheet of steel and wait for equilibrium. One side of the steel is now at the same temperature as the resistor (assuming negligible contact resistance), the other free-air side of the steel is at a lower temperature than the resistor surface but not as low as ambient. So on this side convective cooling will bring the temperature gradient down to ambient. You repeat the experiment but this time the free-air side of the steel is put up against a very very large solid object and again you wait for equilibrium, what will the temperature gradients look like now? Because the solid object is so massive then I imagined the heat flow will cause it's temperature to rise by a negligible amount. Perhaps a small thickness of the solid that's against the steel will have an increased temperature but further into the object this will quickly be brought down to ambient. This feels intuitively right at least. However, if you really wait for equilibrium (which may be a very long time) then the temperature profile across the large solid must be a straight line, from the temperature of the steel on one side to ambient on the other surely? So say half way through the solid, the temperature rise must be significant, is this correct?