In this paper, numerical simulations and measurements of the thermal contact conductance (TCC) at the interface between the plane ends of two cylinders in contact are carried out. The random model of surface roughness is developed, and the non-dimensional basic equations are solved based on a grid system with equi-peripheral intervals in the azimuthal direction that can express reasonably the real contact spot distribution. The effects of the contact pressure, the thermal conductivity of the interstitial medium, and the mean absolute slope of the rough surface on the TCC were clarified by using a network method. In the experiments, four pairs of brass cylinders, each of which has similar surface topology, are used for the TCC measurements. The hysteretic nature of TCC versus contact pressure was observed in the first loading cycle. The present numerical results show that the TCC increases linearly with the mean absolute slope of the surfaces even at the same mean roughness. Such a tendency agrees well with the measurements.