Thermal baseplates are sized to limit high temperature excursions when spacecraft electronics modules are generating peak thermal loads. Because of relatively high nominal conductivity, at low loads makeup heat is required to maintain acceptable temperatures, adding weight associated with batteries, heaters, and thermal control. Thermal switches are systems that are capable of switching between high and low effective conductivity. These systems have been used to eliminate the need for makeup heaters; however, because these systems are electronically driven they add weight in the form of batteries and thermal control. Contact-aided Cellular Compliant Mechanisms (C3M) employ internal contact mechanisms to enable high effective strains in response to mechanical loads. When active, these contacts also introduce new thermal conductive pathways and, using multiple materials, provide a novel avenue to passive thermal control. This paper is concerned with the development of a structure that exhibits effective variable thermal conductivity through its thickness. The proposed concept consists of compliant cells that deform in response to a temperature gradient, alternately creating and breaking heat conduction paths. Initial results indicate that multiple-material C3M devices have the potential to create a large switch ratio between high-conductivity and low-conductivity modes. Complex heat paths through the geometry and thermal characteristc differences between the metal/ceramic pieces help to increase thermal resistance for the low-conductivity mode and generate higher thermal deformation at targeted points.