Hot air rises. When it does, it can’t just leave a vacuum of nothingness behind in the place where it was. Instead, other cooler air gets sucked in from the sides. By definition that air is colder, otherwise that would be the air that’s rising. The result is air on the surface moving from areas of relatively high to low pressure. At an ELI5 level [it looks like this.](https://www.e-education.psu.edu/earth111/sites/www.e-education.psu.edu.earth111/files/Module2/Earth111Mod2GWImage5.png)
So the energy to move the cooler air still came from heat, just in a more indirect way than you were considering.
TLDR: the wind doesn’t blow, it sucks.
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