> “People may think that current flowing in a resistor causes it to heat up, but the Brownian current does not. In fact, if no current was flowing, the resistor would cool down,” Thibado explained. “What we did was reroute the current in the circuit and transform it into something useful.”

Based on this I understood that it'd indeed cool down and create a heat gradient if it wasn't doing any work, but the difference it'd create is instead used to induce a current, which means it probably wouldn't cool down as long as that potential is used in this way instead (?)