There have been extensive previous laboratory studies of thermal convection in a vertical cylindrical annulus of fluid that rotates about its axis with angular velocity Ω (say) with respect to an inertial frame and is subject to an axisymmetric horizontal temperature gradient, as well as associated theoretical and numerical work. The relative flow produced by concomitant buoyancy forces is strongly influenced by Coriolis forces, which give rise to azimuthal circulations and promote, through the process of “baroclinic instàbility”, regimes of non-axisymmetric sloping convection which can be spatially and temporally regular or irregular (“chaotic geostrophic turbulence”). It is also known from previous work that such flows are changed dramatically by the presence of a thin rigid impermeable radial barrier blocking the cross-section of the annulus, and capable of supporting a net azimuthal pressure gradient and associated net azimuthal temperature gradient within the fluid. The presence of the barrier can thus render convective heat transport across the fluid annulus (as measured by the Nusselt number, Nu) virtually independent of Ω (as measured by the so-called Ekman or Taylor number) and dependent only on the Grashof number, G. The present study reports further systematic determinations of heat transport and of velocity and temperature fields in the presence of a radial barrier, with emphasis on the Ω-dependence of the crucially-important net azimuthal temperature gradient supported by the barrier and the physical interpretation of that dependence.