The MIRI cryocooler technology is one of the most interesting advances I've ever heard of. My understanding is that it doesn't require any moving coolant, and it does so by creating a "standing wave" of sorts in the heat transfer chamber, and the heat is removed from the areas of high pressure. Heat continually accumulates to where the "peaks" of pressure are, where it can be transferred away to other parts of the spacecraft to be radiated away into space