In this paper, a numerical simulation by the computer code ABAQUS (6.14) was conducted to study the influence of the thermal conductivity, the interstitial fluid convection coefficient and surface roughness on the thermal contact conductance "TCC" to improve the heat transfer between the materials in contact. In our study, the pairs specimens involved have a thermal conductivity k ranging between 20 w/m• K to 390 w/m• K. The diameter of specimen d is 2 cm, the height L is 8 cm, and the surface roughness Ra is in the range of 5 to 20µm. Results indicated that the surface roughness and thermal conductivity present a power law relationship with heat transfer enhancement between solids in contact. Moreover, the interstitial fluid convection coefficient influences weakly the variation in the thermal contact conductance. The TCC magnitude increase more rapidly with decrease of the specimen's surface roughness when the latters have high thermal conductivity than when they have low thermal conductivity.