Even if we took heat out of the air and used it to generate electricity, all that energy in the electricity ends up as heat again.
As for why we can’t just generate electricity out of nowhere? That’s thermodynamics 2nd law. It basically says that energy will diffuse over time. If you have an area with lots of energy and an area with low energy, over time they will even out in energy. Just like your hot cup of coffee becomes room temperature over time. The inverse is not possible(your cup suddenly taking energy out of the room and becoming hot again), unless if you have an outside influence.
Now we do have a thing called heat pumps. These are machines that use electricity to move heat from A to B regardless of how hot A or B is. The efficiency does depend on it but it works even if B is hotter than A. This is essentially how a refrigerator works, it moves heat from the cold inside, to the hot outside.
If we to use a heat pump connected to the outside, which is basically a reversed AC , and then use that heat to generate electricity well.. I doubt it would be net positive.
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