This paper discusses a detailed computational analysis that illustrated the influences of the magnetic field and external potential on the performance of a high-temperature Hall-effect electric thruster. Uniform and non-uniform magnetic field configurations were examined. The Lorentz force in the x direction, acting on the plasma, was shown to substantially enhance the flow velocity in the non-uniform magnetic field, which indicated that the non-uniform magnetic field was more suitable for Hall-effect electromagnetic acceleration. The static temperature increased with the external potential, especially near the region of cathode. This increment in gas temperature, together with the effect of the Lorentz force, results in the enhancement of the velocity at the front and back of the cathode. However, the Mach number and gas density decreased due to static temperature increases caused by the conversion of more electric power into internal energy. The thrust increased eventually with the increase of the average exit velocity.