Is this a physics question? I don't know.

[digonswine]

4. Here is a belated reply-

think of your house as a sealed unit.
If that is the case-the hotter air is upstairs.
What you want is a way to suck in cooler air to replace the hotter.
My advice is--and this is from experience-
At the far end of your upstairs-that is, from the point furthest from your stairs--put a fan in the window facing outside. Seal this as much as possible.
If you want to cool the downstairs, shut ALL OTHER upstairs windows and open one or two first-story windows that are furthest from the stairs.
If you want to cool a single room-the directions for upstairs stays the same, but you only open the windows in the room you want to cool.
This is the same for up or down-stairs.
Do not expect an immediate result. You should feel the difference within an hour.
Feel free to ask any questions.