A radial temperature distribution is applied to the top of a cylinder of rotating stably stratified fluid. Thermal wind shear drives the interior flow. Linearized theory predicts, and laboratory experiments confirm, that when the stratification is large enough it completely suppresses the Ekman pumping into the interior. The interior velocity field, which is primarily azimuthal, responds by satisfying the no-slip boundary conditions without the need of Ekman layers on the horizontal surfaces. Moreover, for large stratification a thermal boundary layer beneath the top surface traps the thermal disturbance applied at the upper surface. The greatest azimuthal velocity occurs at the base of this layer. Below this layer the azimuthal velocity viscously diffuses downward with thermal wind adjusting the temperature. The Rossby radius of deformation based on this layer depth is the cylinder's radius divided by the square root of the Prandtl number. Detailed measurements of the velocity field generated in the cylinder by the heating are compared with the theory in the case where the Ekman layers are eliminated by stratification. The theory and experiments agree qualitatively well over a range of four orders of magnitude of imposed parameters and over a large parameter range the quantitative comparison is also very good.