I have a indoor heating question for you guys.

I have a 2 story house that gets hot in the upper floor and stays
pretty cool on the ground floor. I have air conditioning which I only
use on really hot days. By the way I installed eyebrow vents that
don't seem to be doing a whole lot. I also have a high ceil living
room and it takes the AC quite a while to really cool the house.

Anyway, I know the theory is to keep all the windows closed when using
the AC, but.........
I have hot air trapped on the second floor. Wouldn't it make sense to
open the upper windows to push the hot air out while the cool AC air
is pumped in? Is this true or am I way off base?