Gas, or any heat source really. Yeah I'm serious - for cooling. A certain Albert Einstein invented it with one of his students, a certain Leo Szilard, and patented it: https://en.wikipedia.org/wiki/Einstein_refrigerator
Yes, you are right, this apparatus is invented. ... and banning it will "push a greater strain on the electric grid" (to use GP words) with the current level of adoption. :-) Really?
No need to ban this kind of fridge - it's already uneconomical compared to electric ones - people won't suddenly go buy one unless they need it to run where electricity isn't available. It's the type installed in most RVs for example, makes sense there.