Numerical methods are essential to understand tribological behaviors since it is difficult to measure directly a closed contact or write representative analytical equations. In this paper, a focus on the complexity of a contact is done with the modeling of thermo-mechanical phenomena in connection with tribological triplet (mechanism, first bodies, third body). Discrete element method is chosen to have a dynamic view of a contact and is interesting to represent both damage of first bodies and cohesion of third ones. Thermo-mechanical models are described for first and third-bodies and are adjusted as a function of continuity of the body. Results regarding damage, rheology and thermal effects are studied as a consequence of cohesion of third body and applied energy by the mechanism (pressure, velocity). Because mechanical and thermal behaviors have a narrow but unclear relationship, a balance between local energy (cohesion of third body) and global energy (applied forces by mechanism) is recommended. Keywords Discrete element method (DEM) Á Thermal contact conductance (TCC) Á Damage Á Third body Á Continuous equivalent media