There is an interesting similar concept using magnetic fields instead of compression - some materials rise considerably in temperature when immersed in a strong magnetic field.

Extract heat to a radiator, turn off the electromagnet, open the coolant circuit valve. It's called Magnetocaloric effect and they were considering it for in-car AC a few years ago, dunno what came of it.

https://en.wikipedia.org/wiki/Magnetic_refrigeration https://www.sciencedirect.com/topics/chemistry/magnetocalori...