AnAlysis of heAt exchAnge in the powertrAin of A roAd vehicle with A retArderAnAlizA wymiAny ciepłA w ukłAdzie nApędowym pojAzdu drogowego z retArderemThe paper presents a heat exchange model for the cooling system of any complex, physical system. Verification of the correctness of the theoretical model was carried out on the example of a vehicle with a combustion engine and additionally equipped with a hydraulic retarder. The results of laboratory tests, which were carried out on an engine test bench, were also performed for the above mentioned powertrain, so as to compare the results of modelling with the results of the tests. Determining the operating parameters of the components of the cooling system aimed at protecting the entire powertrain against overheating is a key task. Theoretical analysis of heat exchange in the powertrain of a road vehicle was carried out, with particular emphasis on the hydraulic retarder (a device braking the vehicle during a descent on roads with a high gradient of the road, mandatory according to the ADR convention). The subject of the study was a mathematical model of a complex cooling system developed by the authors, described by means of balance equations and differential equations. This model was tested with the use of the Matlab-Simulink suite for given load parameters of the cooling system, which were used in tests on an engine test bench. The values of coefficients describing the thermal state of the powertrain were obtained. Simulations were performed for different variants of technical parameters of the expanded cooling system. In this way, individual units and components of the cooling system were optimized so that it fulfilled its role in the assumed operating conditions and the ecologization of emission of energy sources (fuel) and harmful substances.