A wave rotor combustor includes an inlet plate, an outlet plate, and a rotor drum assembly positioned therebetween. The inlet plate is formed to include an inlet port arranged to receive a mixture of fuel and air. The outlet plate is formed to include an outlet port arranged to receive combusted gasses flowing out of the wave rotor combustor. The rotor drum assembly is arranged to rotate relative to the inlet and outlet plates and to combust the fuel and air mixture as part of a combustion process. Conditioned air is passed through the wave rotor combustor to regulate a temperature distribution of the wave rotor combustor.