Thermal control elements, i.e., thermal diodes, switches, and regulators, can control the heat flow in an analogous way in how electronic devices control electrical currents. In particular, a thermal diode allows a larger heat flux in one direction than in the other. This has aroused the interest of researchers working on the thermal management of electronics, refrigeration, and energy conversion. Solid-state thermal diodes are attractive because they are silent, reliable, lightweight, and durable. While some solid-state thermal diodes have been developed at the nano- and microscale, the leap to the macroscale has yet to be made. A macroscale thermal diode would play a crucial role in the future development of applications related to caloric refrigeration and heat pumping. Additionally, the temperature changes of caloric materials (due to the caloric effect) are ideal for testing these thermal devices. This paper aims to numerically evaluate the influence of a macroscopic solid-state thermal diode in a magnetocaloric refrigeration device under transient and quasi-steady-state conditions. Materials with different temperature-dependent properties were analyzed, and the most promising ones were selected for the operating range of a magnetocaloric device (290–296 K). The highest achieved magnetocaloric thermal rectification ratio under transient conditions was up to 295-times higher than with quasi-steady-state operation. This shows that transient operation should be considered for future progress with this technology.