Since it takes different amounts of energy to heat up or cool down different materials...

Won't you have a thermoelectric/Peltier effect, any time you have two separate metals contacting each other, and an ambient temperature change?

So if I forgot a sheet of copper, on top of a sheet of aluminum, and they're in a room that constantly fluctuates in temperature... If there is something to complete the circuit, there's "free" energy there, right?