The thermal environment of a pulse detonation engine was modeled using a space-time averaging procedure. The method allowed the one-dimensional, lumped-capacitance model to be used. The tube dimensions were a bore of 100 mm and a length of 1 m. For the calculations, the PDE pulse was split into a heating, exhaust and purging subprocess. Assumptions for the duration of each process were made based on previous experiments. The PDE was also assumed to operate at about 19 Hz. The calculations were performed for a stoichiometric air and octane mixture initially at STP. Wall materials consist of stainless steel, copper and Haynes alloy. Different water flow rates and jacket radii were used. The study showed that high water flow rates and large jackets were able to reduce the temperature at the water jacket. The temperatures of the inner and outer PDE walls were unaffected by the coolant flow or the jacket dimensions. These surfaces remain at high temperatures and indicate that a PDE requires advanced cooling techniques. For this configuration with stainless steel surfaces, the PDE wall temperatures were still rising albeit slowly after 12000 cycles.