In order to bring magnetocaloric technology to new markets in the future several obstacles have to be overcome. One of the most important issues that represent a serious obstacle in the existing prototypes is the low operating frequency, which directly affects the low power density of the device. A potential solution is the introduction of new heat-transport mechanisms. One of such solutions is described in this article. It is the application of a new type of magnetic refrigeration device, based on solid-state thermoelectric thermal diodes with embodied thin-plate magnetocaloric materials. Thermal diodes can provide a very fast heat transport from or to the magnetocaloric material. A quasi 2-D numerical model of the device was developed. This model serves for dynamic heat transfer simulations of magnetocaloric devices, which apply thermal diodes. The analysis considers different operating and geometrical characteristics and gives important information about the performance and operating mechanisms of such a device. Results show capabilities of potential devices' operation at high operating frequencies (one or two orders higher than existing magnetocaloric devices) with corresponding high specific powers (per mass of the MCM) and relatively high efficiencies.