Consideration of the heat transfer effects in low-heat-rejection engines has prompted further study into engine heat transfer phenomena. In a previous study, an approximate solution of the one-dimensional energy equation was acquired for transient, compressible, low-Mach number, turbulent boundary layers typical of those found in engines. The current study shows that an approximate solution of the one-dimensional energy equation with arbitrarily-distributed heat release can also be obtained.Using this model, the effects of high temperature walls, combustion, and autoignition on heat transfer can be studied. In the case of high temperature walls, the model predicts the expected behavior unless the quench distance gets very small. For combustion, the reaction must occur close to the wall for a direct effect on the heat transfer to be observed. With autoignition, instantaneous values of heat flux reach levels as high as 6 MW/m2, and oscillate in phase with the pressure wave.Finally, a method for using this model for global heat transfer predictions is suggested.