Auxiliary braking systems, which include also the Jake brake system, have a decisive role in issues such as road safety and optimization of fuel consumption. These issues are raised especially for heavy vehicles such as trucks or buses. One of the most delicate problems encountered when designing such a braking mechanism is to accurately evaluate the thermal conditions present in the combustion chamber. Failure to know and control these conditions can lead to deteriorations of injection system components, such as the injectors, which are no longer cooled by fuel. The present paper aims to advance a simple and quite accurate mathematical model to describe the processes occurring in a Jake brake system. Such a model can be very interesting when high power diesel engines are designed.