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.
Yep, I had all my windows and doors open.
Not sure then. Maybe concrete really is too hot. Where I am adobe (clay, not company) buildings have traditionally been used in some areas to even out temperatures (desert region. Too hot in the day, too cold at night).