Despite substantial theoretical studies of thermal contact conductance in the past, the application of statistical mechanics in this field has never been attempted. This paper addresses contact conductance from macroscopic and microscopic viewpoints in order to demonstrate the promise of the statistical mechanics approach. In the first part of the derivation, the Boltzmann statistical model is applied to determine the most probable distribution of asperity heights for a homogeneously, isotropically rough surface. The result found is equivalent to Gaussian distribution, which has only been assumed but not rigorously substantiated in the past. Subsequently, the Boltzmann statistical model is applied to predict the distribution of true contact spots when two such surfaces are pressed together, resulting in a relationship between the total thermal contact conductance and the relative interfacial pressure. The numerical results are compared to published empirical data, and a good order-of-magnitude agreement is found.