Various theories have been formulated to predict thermal contact resistance but agreement with experiments has been variable when very smooth surfaces are involved. The guarded hot plate method for thermal conductivity measurements was chosen to determine temperature drops across interfaces. It was shown that a general theory can be modified to give a good estimation of the thermal resistance with a variety of interface materials. The effects of pressure, material hardness, surface roughness, and thermal properties of the interface material on thermal resistance between two smooth steel surfaces were studied. Air, Cu,In and Teflon foils, a silicone oil based heat sink compound and Ag filled paint were studied. The theory predicts temperature discontinuities when solids, fluids or gases are present in the interface.