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This paper presents studies on thermal contact conductance at light contact loads. Surface profilometry measurements are presented which show that actual surface asperity height distributions are not perfectly Gaussian. The highest asperities are truncated, causing existing thermal contact conductance models to underpredict experimental data. These observations have been incorporated into modifications of existing contact conductance models. The truncation leads to an enhancement of thermal contact conductance at light contact pressures. The preliminary model has been compared against thermal contact conductance data presented in the open literature, and good agreement is observed. The results show that the truncation is a function of the roughness level: the rougher the surface, the more truncated the surface height distribution.