The control of heat transfer is a key challenge in modern technology. This has always been the case for traditional heating or cooling devices, such as heat exchangers and re- frigerators, but has nowadays also proved crucial for e.g. the longevity of electronics, the performance of advanced manufacturing processes, the energy consumption of high- performance computing or data storage clusters and space applications. Traditionally, the thermal properties of such systems are controlled via linear and passive thermal compo- nents, whose thermal properties are mainly governed by their static thermal conductivity and size. However, there has recently been a growing interest in components that har- ness switchable and nonlinear heat transfer mechanisms to obtain tunable heat transfer control, referred to as thermal regulators, which can realize advanced components such as thermal diodes and switches [1]. In this study, we propose a systematic and efficient way of designing thermal regulators via topology optimization. For efficiency and reliability, we utilize gradient-based mathe- matical optimization algorithms to update the material distribution, where the gradients are obtained using the adjoint method. To model the thermo-mechanical interactions that occur in the switch during actuation, a fully coupled non-linear thermo-mechanical numerical analysis is solved based on the finite element method. One hurdle to the system- atic design of contact utilizing thermal regulators is their inherent modeling complexity. Contact is intrinsically a highly non-linear and non-differentiable problem, which results in ill-convergence of the gradient-based optimization algorithms. Recently, [2] proved that the so-called third medium contact method is an excellent fit for topology optimization of contact-aided mechanisms. This contact model approximates contact pressures via the reactive tractions that occur when a third medium, that is placed in between the contacting surfaces, is compressed. In this work, we further extend the prospect of the third medium contact method to the problem of heat transfer between bodies in contact, such that we now want a third medium that transfers heat when contact occurs, but otherwise acts as an isolating material.