> The hot air flowing from outside through your windows could be compressed making it cool.
Compressing air actually makes it hotter, but that's not what's happening. Forcing air through a smaller space makes it flow faster, which ironically makes it less dense -- and hence colder.
It's the same effect that people claim holds airplanes up. (But doesn't. That's mostly the angle of attack.)
Alternatively, you could power an A/C with a micro wind turbine. Both have the same problem: no wind, no cooling. I'm currently in 30ºC and the tree leaves barely move.
The hot air flowing from outside through your windows could be compressed making it cool.
I wonder if there are existing, not so ugly commercial products providing that. This could be a green alternative for air-conditioning.