With the world’s increasing usage of electronic devices such as mobile devices and batteries, improving the reliability and performance of these devices has become more and more important. Besides the common overheating issues, low-temperature environments can also cause performance degradation or failure to these devices. Research on thermal switches and thermal regulators aims to improve the thermal management of electronic devices across a range of operating conditions. However, continuous tuning of thermal transport with all-solid-state systems is still challenging. The primary purpose of this work is to propose and demonstrate compressible foams as novel variable thermal resistors and thermal regulators to control device temperature under various input heat flux and ambient temperature. The graphene/PDMS foam is first tested in this work to demonstrate promising performance as a thermal regulator, with continuous tuning capability and a system switching ratio over ~4. Then, the dependence of the thermal conductivity of polymer foams during compression is studied, where the thermal conductivity is measured using a customized system based on an infrared microscope. Unexpectedly, the thermal conductivity decreases slightly at a compression level of more than 10x, in contrast to common theories that the thermal conductivity would increase with the mass density. A simple “spring model” is proposed as a limit where the ligaments do not build contacts during compression. Our results now fall in between the “spring model” and other common theories and can be explained. To gain further insights, a molecular dynamic simulation is performed on a graphene random nanofoam on the nanoscale. The result also shows that the effective thermal conductivity along the compression direction is not sensitive to the mass density, consistent with our experimental data on the macroscopic scale. This work provides useful insights into dynamic thermal management of electronic devices.