Numerical simulation has been carried out to investigate the influence of radial temperature gradient on the Circular-Couette flow. Varying the Grashof number, we study the detailed flow and temperature fields. The current numerical results show good agreement with the analytical and experimental results currently available. It turns out that spiral vortices are generated by increasing temperature gradient. We classify the flow patterns for various Grashof number based on the characteristics of flow fields and spiral vortices. The correlation between Richardson number with wave number shows that the spiral angle and size of spiral vortices increase with increasing Richardson number.