The temperature distribution on an inner wall of a rotating detonation engine is analysed numerically by applying the extended heat transport equation. This heat equation, in form of Fourier’s and Christov-Cattaneo’s theories, is presented in a moving frame. With the latter theory, the second sound in a solid, as a propagating heat wave, is described and its speed is computed. The equations are discretised in space by the finite element method and the linear system of equation is integrated in time using the \(\Theta \) scheme. The domain of interest is simulated and the solutions of both heat transport equations are compared. Results indicate differences in the microscale frame and further work must be carried out.