The radial growth of compressor discs is strongly influenced by conjugate heat transfer between conduction in the co-rotating discs and buoyancy-driven convection in the rotating fluid core between the discs. An accurate prediction of metal temperatures of these discs is an important issue in thermo-mechanical design, where blade-tip clearances must be controlled carefully to ensure safety and efficiency under all operating conditions. This paper presents an experimental study of the fluid dynamics and heat transfer in a closed rotating cavity, comparing results with theoretical models and introducing a new compressibility parameter x. At large values of x, where compressibility effects are significant, the air temperature approaches that of the shroud; such conditions suppress buoyancy effects and the flow in the rotating cavity becomes stratified, with convection replaced by conduction inside the fluid core. There are important practical consequences of stratification with significant differences in temperature distributions and stresses inside compressor discs. The influence of x is also shown on the radial temperature distributions for the discs and on the shroud heat transfer correlations, which are compared qualitatively with previously published data collected where the effects of compressibility are relatively small. The experiments reveal that there is a critical value of x where the convective heat flux to the shroud is zero. The radial distribution of disc temperature was that expected from pure conduction in a cylinder. A new heat transfer correlation based on measured shroud heat flux and the theoretical core temperature is presented. The unsteady flow characteristics in the cavity were also investigated, identifying coherent rotating structures across a range of experimental conditions. These cyclonic / anticyclonic vortex pairs generate the non-dimensional circumferential pressure difference necessary for the radial outflow (of cold fluid) and inflow (of hot fluid) through the rotating core. The experiments show the magnitude of these pressure variations can be correlated against Grashof number and that at high values of x the structures do not exist. The combined experimental and theoretical results will be of practical interest to engine designers and for the validation of computational models.