I proposed some exotic biochemistry on the Worldbuilding stack. https://worldbuilding.stackexchange.com/questions/166814/digestive-system-of-the-ultimate-omnivore/166829#166829
Your creature oxidizes molecules in its "stomach" which is more of a furnace. Anything that can be oxidized is fair game - any reduced carbon, or nitrogen, or metal salt. Oxidation produces heat. The amount of heat produced is controlled by controlling oxygen ingress to the stomach.
Under hot conditions, certain metalloproteins change configuration. The circulation brings these proteins into hot conditions near the stomach and they capture heat energy with the configuration change. When the hot-configured metalloprotein circulates out to the cold exterior (possibly radiator plates or fins) it shifts back to the cold configuration. This conformational shift is linked to an ATPase and generates ATP for the creature to use for its muscles and metabolic processes, as Earth life does.
I was challenged to produce a molecule which could capture and release energy in this way. Molecules do this all the time with a phase change - that is a steam engine. But is there any example of a molecule (or a whole type, perhaps) which undergoes a conformational change with heat that it later discharges in a controlled manner, with an exothermic relaxation back to the cold conformation. Not necessarily a biomolecule.