I would have loved to see that video 2 months ago. Thanks for sharing.

I tried to put the same kind of desk fan at the window, one way and then the other, for a few hours, to see if it had any effect. It was a very hot day but colder outside than inside. The building's concrete was likely still radiating the heat from the day before and there was no wind.

I see now that my observation at the time was right: it did nothing to the temperature, and it might have worked better if I had put the fan 1-2 meters away from the window, directing it towards the window. Now, whether the effect would have been significant anyway… we'll have to wait for next summer to know, I guess. I'm not particularly looking forward to it, though.

A 20 or 24" box fan still moves a LOT of air- you should get a decent breeze if you guide the air. the largest mistake I see is forgetting that a fan can't blow if theres no air coming or going- you need openings of equal size (larger is better) between where the fan is and where you want the air to come from/go.

An easy mental model is imaging the air is water. Close a door on a room and it'll fill up and block the hose.

PS: a box fan and a 5" thick MERV13 filter makes a heck of an air filter. 2" likely also will work. MERV13 is great, but some HVAC can't handle it, and it takes a couple passes (term is air exchanges per hour, I think) to capture what HEPA does in a single pass.