Heat transfer within the rotating compressor cavity of an aero-engine is predominantly governed by buoyancy, which can be characterized by the Grashof number. Unsteady and unstable buoyancy-induced flow structures influence the temperatures and stresses in the compressor rotors, and these affect the radial growth of the disks. In addition, the heat transfer from the disks and shroud increases the temperature of the throughflow of cooling air. This paper contains two connected parts. First, a heat transfer correlation for the shroud of a rotating cavity was determined from steady-state heat flux measurements collected in the bath compressor-cavity rig at engine-simulated conditions. The Nusselt numbers were based on the cavity air temperature adjacent to the shroud, which was predicted using the Owen–Tang buoyancy model. Heat transfer from the shroud was consistent with free convection from a horizontal plate in a gravitational field. Maximum likelihood estimation was used with a Rayleigh–Bénard equation to correlate the shroud Nusselt number with the local Grashof number. Second, an energy balance was used to calculate the enthalpy rise of the axial throughflow from the measured disk and shroud heat fluxes. Disk fluxes were derived from radial distributions of measured steady-state disk temperatures using a Bayesian model and the equations for a circular fin. The calculated throughflow temperature rise was consistent with direct thermocouple measurements. The complex, three-dimensional flow near the cavity entrance can result in enthalpy exchange penetrating upstream in the throughflow, and rotationally induced flow can create upstream axial flow in the outer part of the annulus.