Two-dimensional stress waves in an elastic circular cylinder with a thermal gradient were analyzed numerically when an axisymmetric impulsive load was applied to the end face of the cylinder heated (or cooled) to produce a thermal distribution. For numerical analysis, the finite difference method based on integration along bicharacteristics was employed. By obtaining the numerical results for the cases of various temperature profiles and impact loading conditions, it is clearly demonstrated that stress wave propagation is affected by the thermal gradient, and that when the thermal gradient in the pressure bars of the split Hopkinson bar becomes steeper, experimental results by the conventional method contain more noticeable errors.