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This paper presents a study on the thermoelastic contact between a wavy surface and a flat surface in the presence of a heat-conducting interstitial medium in interface gaps. The influence of applied mechanical and thermal loads on the deformation of the gaps is taken into account. The contact problem is reduced to a system of singular integro-differential equations for a temperature jump across the gaps and the height of the gaps. Solutions are obtained for the cases of thermoinsulated and heat-conducting gaps. It is shown that, in contrast to the thermoinsulated gap model, the use of the heat-conducting gap model makes it possible to construct a physically correct solution of the contact problem. It is revealed that the wavy interface with heat-conducting gaps exhibits thermal rectification. The effects of the medium’s thermal conductivity, the pressure and heat flow magnitudes and the waviness amplitude on the effective thermal contact resistance and the level of thermal rectification are analysed.