Posted By: fostertomTell me if I'm wrong, but the inboard one-third of the conductive screw will be kept pretty much warm by its contact with the warm interior; likewise the outboard one-third will be kept pretty cold by its contact with the cold exterior. Most of the temp gradient along the length of the screw will be concentrated in the middle third.

Sorry to be blunt, but you're wrong. Assuming the screw is uniform in cross-section the temperature gradient will be linear. There's nothing special about the middle third of the screw which allows it to support a higher thermal gradient for the same heat flow.

Tom, If you think about it. Each of the materials in your example has a temperature gradient flowing from hot to cold. This being the case, each gradient is linear, so no side to side heat loss from a more conductive to less conductive material, within the wall make up. Of if you wanted to argue that the fixing was hotter than the surrounding insulation - and that heat was lost into the insulation on its way to the colder outside - then the heat lost into the insulation would replace heat which would otherwise have been lost into the insulation from its inboard surface. Irrespective of the heat path or paths the heat lost would be proportionate to the surface areas of each material.

Obviously we are talking about a construction with homogeneous layers here