This study presents numerical solutions of the two-dimensional Navier-Stokes equations for supersonic unsteady flow in a convergent-divergent nozzle with heat addition. The TVD scheme in generalized coordinates is employed in order to calculate the moving shock waves caused by thermal choking. We discuss on transient characteristics, start and unstart phenomena, fluctuations of specific thrust caused by thermal choking and viscous effects. We prove that the control of separation of boundary layer is the most important key problem to prevent the thermal choking.