A heat pump is provided that uses multiple stages of MCMs to cause heat transfer between a heat receiving end and a heat transmitting end. Thermal blocks are placed along the direction of heat transfer at locations in the heat pump that preclude the transfer of heat in a direction from the heat transmitting end towards the heat receiving end. The heat pump can be, for example, part of a refrigeration loop or can be connected directly with the object for which heating or cooling is desired. An appliance incorporating such a heat pump is also provided.