Results of a room temperature magnetic refrigeration test bed and an analysis using a computational model are presented. A detailed demonstration of the four sequential processes in the transient magnetocaloric regeneration process of a magnetic material is presented. The temperature profile during the transient approach to steady state operation was measured in detail. A 5 °C evolution of the difference of temperature between the hot end and the cold end of the magnetocaloric bed due to regeneration is reported. A model is developed for the heat transfer and fluid mechanics of the four sequential processes in each cycle of thermal wave propagation in the regenerative bed combined with the magnetocaloric effect. The basic equations that can be used in simulation of magnetic refrigeration systems are derived and the design parameters are discussed.