The key is pulling a fresh sample of air over the sensor. In the case of the 5n1 design, that has to be done with a fan. That's why added power, either through extra solar panels or a wired supply, simply works.
You don't need to cool the whole 5n1 body, just bring a fresh sample of air to the sensor.
I'm not going to argue the thermodynamics of the situation with you.
It's as pointless as arguing the angle of the sun, 93,000,000 miles away, doesn't change significantly when you move 4300 feet in altitude.