A simple theory is presented for steady geostrophic circulation of a stratified fluid in a rectangular basin with a circumpolar connection. The interior flow obeys the β-plane Sverdrup vorticity balance, and the circulation is closed by geostrophic boundary currents. The circulation is forced by surface thermal gradients and wind-driven Ekman transport near the latitudes of the circumpolar connection. A thermal circumpolar current arises in response to imposed surface thermal gradients and northward Ekman transport across the gap latitudes. The transport of this model circumpolar current depends on the imposed surface thermal gradients and the gap geometry, but not on the strength of the wind forcing. In contrast, the circulation induced in a related reduced-gravity model by Sverdrup transport into the gap latitudes has zero zonally integrated zonal transport. The thermal current arises as a consequence of the geostrophic constraint, which requires that the northern region fill with warm fluid until it reaches the sill depth, where return geostrophic flow can be supported. Thus, the structure of the middepth, midlatitude thermocline is directly influenced by the geometry of the gap. A similar constraint evidently operates in the Southern Ocean
