Heyo
In the summer, I stick box-fans in the windows, pulling in nice cool air and pushing off the use of AC by a couple months
Of course, since these are cheap CT fans, all they have is a rotary dial (0-3), and no real ability to automate.
I decided to add a 3 channel controller on AliExpress
Since my goal is high WAF, everything needs to work via the orinal controls. This allowed me to still use the original rotary dial, while giving me a HA override
Installation was fine, largest annoyance was the fan was original a switched neutral. Once I figured that out, I moved to a switch hot layout, and the tested. Turned on fan... Err, fine.
Threw in shoe glue as adhesive, and wire protection, and put 'er back together
Could be worth trying
One advantage of sucking air In from outside is that that causes it to pull itself tight against the mosquito net, so it's less likely to fall over.