The source-sink flow within a rapidly rotating annular region, bounded by a pair of concentric circular cylinders and by horizontal end plates, is considered. Fluid is injected into the container at arbitrary locations on the inner radius and withdrawn at one or more locations on either the inner or outer radius, through axisymmetric slots. The upper end wall is maintained at a higher constant temperature than the bottom end plate, while the vertical side walls are thermally insulated; the entire apparatus is rapidly rotating about the common axis of the cylinders. An analysis of the flow and temperature distribution is carried out in the context of the Boussinesq approximation and by assuming that vertical buoyancy effects are negligible to leading order. A method for calculation of the temperature distribution within the container is developed for physical situations where the effects of the imposed thermal gradient and the source-sink flow are of comparable magnitudes; the procedure is applicable for an arbitrary distribution of sources and sinks on the side walls. The temperature problem is an unusual complicated boundary-value problem, and numerical solutions are obtained for a number of different cases. The results reveal a number of interesting flows and temperature fields within the container and indicate how the temperature field is influenced by the placement and temperature of the sources and sinks, as well as by the relative magnitudes of the imposed forced flow and vertical thermal gradient. The possible application of the present theory to centrifuges is indicated.