The clearance of compressor blade tips during aero-engine accelerations is an important design issue for next-generation engine architectures. The transient clearance depends on the radial expansion of the compressor discs, which is directly coupled to conjugate heat transfer in co-rotating discs governed by unsteady and unstable buoyancy-induced flow. This paper discusses an experimental and modeling study using the Bath Compressor Cavity Rig, which simulates a generic axial compressor at fluid-dynamically scaled conditions. The rig was specifically designed to generate heat transfer of practical interest to the engine designer and validate computational codes. This work presents the first study of the fundamental fluid dynamic and heat transfer phenomena under transient conditions. The rotating flow structure was seen to be characterized by coherent pairs of cyclonic/anticyclonic vortex pairs; the strength, rotational frequency, stability, and number of these unsteady structures changed with changing rotational Reynolds and Grashof numbers during the transients. These structures, measured by unsteady pressure transducers in the rotating frame of reference, were only present when the flow in the rotating cavity was dominated by buoyancy. Experimental correlations of both Nusselt number and radial mass flowrate in the rotating core were correlated against Grashof number. Remarkably, the experiments revealed a consistent correlation for both steady-state and transient conditions over a wide range of Gr. The results have a practical application to thermo-mechanical models for engine design.