Magnetic refrigeration as an alternative for vapor-compression technology has been the subject of many recent studies. Most of the studies focus on systems with limited cycle frequency in which a fluid transfers heat to and from the magnetocaloric material. A suggested solution for increasing the frequency is use of solid-state magnetic refrigeration in which thermal diodes guide the heat from the cold end to the warm end. In this work a solid-state refrigeration system with Peltier elements as thermal diodes is modeled in details unprecedented. The performance of Peltier elements and magnetocaloric materials under their transient working conditions after reaching cyclic steady state are simulated by two separate computer models using finit...