This Paper presents numerical solutions of two-dimensional Euler equations for supersonic steady and unsteady flows with heat addition in a convergent-divergent duct, The Van Leer FVS (flux vector splitting) method in generalized coordinates is employed in order to calculate the inviscid strong shock waves caused by thermal choking. We discuss on transient characteristics, start and unstart phenomena caused by thermal choking, limit of equivalence ratio to avoid thermal choking and fluctuation of specific thrust caused by thermal choking. We prove that thermal choking is a serious problem in view of engine performance.