Heat pumps (like AC units, fridges, etc) become less efficient the greater temperature difference they have to pump the heat. So pumping heat from a 25°C room to a >100°C steam engine would become terribly inefficient. It would need more energy, which creates more environmental damage and climate crisis to source, and that energy heats the cities even more.

The only sane way to cool cities is to get rid of as much concrete and asphalt as possible (especially the vast amounts of ground that is covered for cars), and keep only narrower sealed paths for small individial transport like bikes. Plaster everything with trees and grass and other greens. They cool down the city dramatically and are able to take up the water that comes down at extreme weather events.

Escaping the urban hellscape cannot be achieved by building more stuff and throwing more energy at it. Just visit a park in your city and observe how the temperature changes, it is that simple. Mobility cannot seal all surface area, it has the be minimal, i.e. narrow paths and trains with rails that can also run on open ground / green areas. This implies of course not building secluded areas for living, shopping, working etc.. It has to be a mix, where commutes are short (i.e. like european cities, not american ones).

https://en.m.wikipedia.org/wiki/Organic_Rankine_cycle

That's basically what this engine cycles doing. It's taking heat from some source and trying to save as much energy as it can. Looking at efficiencies around 40 to 60%.

The greater the thermal gradient the easier it is to produce useful energy from it.

There is a lot of bogus "science" out there, and this is part of it.

You need a temperature differential to harvest electric energy. You also need a differential to get heat energy to flow (usually from inside your apartment to outside). If you have that differential, you do not need an AC, you just open the window. If you do not have a differential (or if it points the wrong way, i.e. outside is hotter than inside), you need an AC + energy to create that differential, that lets thermal energy flow from your room to outside. There's no "free leftover differential" in this, the differential it creates is literally to transport heat energy = why you have turned on the AC. Every bit you use of this differential for harvesting energy, you could turn down the AC a notch and have it save more energy than you could possibly harvest.

This idea is as mute as mounting a wind turbine to your electric car to "harvest" the headwind from driving