jats:pDirect numerical simulations are used to investigate the nature of fully resolved small-scale convection and its role in large-scale circulation in a rotating jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112019000648_inline1" />jats:tex-math$f$</jats:tex-math></jats:alternatives></jats:inline-formula>-plane rectangular basin with imposed surface temperature difference. The large-scale circulation has a horizontal geostrophic component and a deep vertical overturning. This paper focuses on convective circulation with no wind stress, and buoyancy forcing sufficiently strong to ensure turbulent convection within the thermal boundary layer (horizontal Rayleigh numbers jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112019000648_inline2" />jats:tex-math$Ra\approx 1012-1013$</jats:tex-math></jats:alternatives></jats:inline-formula>). The dynamics are found to depend on the value of a convective Rossby number, jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112019000648_inline3" />jats:tex-math$Ro\Delta T$</jats:tex-math></jats:alternatives></jats:inline-formula>, which represents the strength of buoyancy forcing relative to Coriolis forces. Vertical convection shifts from a mean endwall plume under weak rotation (jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112019000648_inline4" />jats:tex-math$Ro\_\{\backslash unicode[STIX]\{x0394\}T\}>10^\{-1\}$</jats:tex-math></jats:alternatives></jats:inline-formula>) to ‘open ocean’ chimney convection plus mean vertical plumes at the side boundaries under strong rotation (jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112019000648_inline5" />jats:tex-math$Ro\_\{\backslash unicode[STIX]\{x0394\}T\}<10^\{-1\}$</jats:tex-math></jats:alternatives></jats:inline-formula>). The overall heat throughput, horizontal gyre transport and zonally integrated overturning transport are then consistent with scaling predictions for flow constrained by thermal wind balance in the thermal boundary layer coupled to vertical advection–diffusion balance in the boundary layer. For small Rossby numbers relevant to circulation in an ocean basin, vertical heat transport from the surface layer into the deep interior occurs mostly in ‘open ocean’ chimney convection while most vertical mass transport is against the side boundaries. Both heat throughput and the mean circulation (in geostrophic gyres, boundary currents and overturning) are reduced by geostrophic constraints.</jats:p>