Thermal management is a fundamental concern for spacecraft. The temperatures of electronic “black boxes” associated with systems and payloads must be maintained within an acceptable operating range in the presence of significant variations in thermal loading. To achieve thermal control, the goal of this research is to design a passive device that modulates the heat transfer between the electronic boxes and the thermal bus. The design of this interface is based on cellular contact-aided compliant mechanisms (C3M), which deform under changing thermal conditions. Thermal control is achieved by using C3M that are made of two materials with different thermo-mechanical properties: one material has a high positive coefficient of thermal expansion (CTE) and thermal conductivity, while the other has a low or slightly negative CTE and low thermal conductivity. These materials expand or contract differently under changing temperatures and, as a result, modify the normal pressures at contact interfaces, affecting the net heat flux. This paper investigates a topology optimization method that tackles this problem by generating optimal designs for specified thermal conditions. A key feature of the design approach is the inclusion of a unilateral contact thermal resistance model at contact interfaces in a thermo-mechanical topology optimization problem. Optimal designs have been generated using a three-phase (two-material plus void) topology optimization algorithm. The algorithm successfully reproduced results available in the literature. The definition of the objective function is a central concept for the design of the C3Ms. The choice of a satisfying objective function that would enhance the conductive performance of the C3Ms should also trigger a good numerical response of the optimization process to provide effective topologies.