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.