A numerical study is performed on the swirling flows driven by the rotating top disk in a cylindrical container. The top disk is heated and the bottom disk is cooled, while the sidewall is assumed as adiabatic, and the Boussinesq approximation is adopted. The flows are studied for wide ranges of the governing parameters, the Reynolds number, the cylinder aspect ratio, the stratification parameter, and the Prandtl number. The occurrence of the vortex breakdown is studied and the results are plotted in a form of flow patter diagrams.