In this paper, a model for calculation of the temperature distribution in the metal tribopair barplane in the conditions of dry friction is developed. A model for solving of the problem of thermoelasticity for a metal bar under uniaxial tension-compression is also proposed. A simulation of the interaction between the bar and the plane was carried out taking into consideration various conditions, such as ambient temperature and linear dimensions of the contacting pairs. The simulation results showed that the distribution of the thermal field nonlinearly depends on the linear dimensions of the body, but the frictional heating in the first counter-body can be compensated by small changes of the linear dimensions. When calculating the stress-strain state of the bar, a non-linear dependence of the stress in the bar was obtained, which is due to the presence of contact pressure. The modelling results were proved experimentally with the use of the friction machine MTU-1. The results of the work can help us predict frictional heating for metal tribopairs and decrease its negative consequences.