The change in compressor blade-tip clearance across the flight cycle depends on the expansion of the rotor, which in turn depends on the temperature and stress in the discs. The radial distribution of temperature is directly coupled to the buoyancy-driven flow and heat transfer in the rotating disc cavities. This paper describes a new test rig specifically designed to investigate this conjugate phenomenon. The rig test section includes four rotating discs enclosing three cavities. Two discs in the central cavity are instrumented with thermocouples to provide the radial distribution of temperature; the two outer cavities are thermally insulated to create appropriate boundary conditions for the heat transfer analysis. An axial throughflow of air is supplied between a stationary shaft and the bore of the discs. The temperature of the throughflow air is measured by thermocouples in rakes upstream and downstream of the central cavity. For a cold throughflow, the outer shroud of the central cavity is heated. Two independently-controlled radiant heaters allow differential shroud temperatures for the upstream and downstream discs, as found in aero-engine compressors. Alternatively, the throughflow can be heated above the shroud temperature to simulate the transient conditions during engine operation where stratified flow can occur inside the cavity. The rig is designed to operate in conditions where both convective and radiative heat transfer dominate; all internal surfaces of the cavity are painted matt black to allow the accurate calculation of the radiant heat transfer. Separate attachments can be fitted to the cobs of both central discs; the attachments reduce the axial gap between the cobs — reducing the gap to zero creates a closed cavity, which can occur in some compressor designs. Other instrumentation includes heat-flux gauges on the shroud and high-frequency pressure transducers embedded into the disc diaphragm to capture unsteady flow structures. Attention has been given to experimental uncertainty, including the computation of the thermal-disturbance errors, caused by thermocouples embedded in the rotating discs; a Bayesian statistical model is used to reduce the effect of uncertainties in temperature measurements on the calculation of the Nusselt number. The effect of relevant non-dimensional parameters on the radial distribution of the disc and throughflow temperatures has been shown for some typical cases.