Will opening more windows help keep my computer cool?

If the windows not in the same room then No.....

"No" ...  it will put more strain on the CPU and cause it's temperature to rise.
            Close any windows that you're not presently using ... a good rule of thumb.

A little, but the best way for my laptop was getting it off the base and putting it on a stand that I used to cook cookies on.  This way the heat flows away from the machine and I have had no overheating problems at alli since then. 

I used to think I would have to get a new computer, but that was at least 8 months ago.  I am gratified that I don't have to worry about that expense right now.

I think will only heat your computer more;))

it depends on how open the case is.  If the components are on a bench then yes, if not you should either add more fans in the case and that will help it keep the computer cooler.

it might