A three-dimensional numerical model using the finite volume method was developed to calculate the steady-state temperatures and the thermal contact resistance between two sliding bodies: one is rough and stationary, the other is smooth and moving at a velocity V. The roughness is represented by square-shaped asperities characterized by a parameter epsilon. Heat transfers through interstitial gaps are not taken into account. The numerical methodology was particularly studied in order to reduce the computation time and obtain accurate results. This model was validated by comparison of results with those of an analytical solution.