This thesis describes an experimental study of the transient heat transfer from both a free disc and a rotating cavity. Measured disc surface temperatures - from heating, cooling and quasi-steady tests - were used as boundary conditions for the solution of Fourier's conduction equation. The local and average Nusselt numbers were obtained from the computed temperature distribution, inside the disc, at each time-step. A finite element model was used to predict the thermocouple disturbance errors in the measured Nusselt numbers. The experimental technique was verified using a free disc, which comprised a 762 mm diameter, steel disc rotating in air at speeds of up to 3000 rev/min. For the free disc, the experimental results from the cooling tests were found to be less affected by thermocouple disturbance errors than those from the heating or quasi-steady tests. The measured Nusselt numbers from the cooling tests were in close agreement with established theoretical correlations. The rotating cavity comprised two steel discs, 762 mm in diameter, separated by an axial distance of 102 mm, and bounded at the circumference by an outer shroud. The cavity was supplied with a radial outflow of air, with a maximum flow rate of 0.6 kg/s, and rotated at speeds of up to 2000 rev/min. In some tests, known as the 0.1 radius ratio tests, air entered the cavity axially, through a central inlet pipe of 38.1 mm radius. In other tests, known as the 0.5 radius ratio tests, air entered the cavity axially, but a porous inner shroud was located inside the cavity at a radius of 190 mm. For the rotating cavity, flow visualisation showed the flow structure to consist of an inner source region, Ekman layers on each disc and an outer sink region. The size of the source region was found to depend on the radius ratio, and could be predicted by a simple theoretical model. For the 0.1 radius ratio tests, three regimes of heat transfer have been identified: the 'wall jet', the 'free disc' and the 'Ekman layer' regimes. The measured Nusselt numbers in those regimes were consistent with available experimental and theoretical expressions. For the 0.5 radius ratio tests, the wall jet and free disc regimes were not observed, and the heat transfer in the Ekman layers was found to be lower than for the 0.1 radius ratio cavity.