From what I was told in (southern USA) schools, when things heat up the molecules move faster and are father apart (think of steam, or how metal expands when hot). The molecules cannot move that fast and stay apart forever (that requires energy to maintain), so they will start to slow down and come back together and that’s called “cooling down” or getting “colder”.
So I’m not sure you can harvest energy from something that’s cooling down. Steam engines harvest energy from the pressure buildup of water turning into steam (expanding), and that pressure can generate mechanical energy. In that process the steam dissipates its heat and cools back down into water.
Theoretically you could harvest energy (in my mind and limited knowledge) from something cooling down by heating up metal that expands alot, and you harvest the energy from the moving metal as it cools down and shrinks. The shrinkage/expansion is what could create mechanical movement.
Anyone feel free to correct me if I’m wrong, I’m pretty sure my high-school science wasn’t exactly top tier.
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