The performance of pulse detonation engines (PDE) implies that they have to undergo very extreme cycles where the temperature may rise above 3000 K. The detonation principle, theoretically predicted by the ZND condition, results in a very high energy release at a very high rate, this is why it is very important to account for the heat transfer from the flow to the solid parts of the engine. This compromises the integrity of the vehicle upon which such engine be mounted on, so this work will allow for future researches to design a proper cooling system. This work was aimed to study such heat transfer numerically. The experiments simulated one cycle of the PDE where the initial conditions were in all the cases the same: a homogeneous 25% Hydrogen-air mixture. Different mesh refinements were tried in order to compare the different results for heat transfer. The refined meshes were able to capture the development of the thermal and boundary layers. A second comparison was established between the two boundary conditions that were tried: adiabatic wall and isothermal wall, and it was possible to see the increase of heat flux if the engine had a cooling system