My first house was one of those little 50's era ranch homes. It was in Dallas, TX, where it got REALLY hot in the summer. The house had central air, but it also had an attic fan, which was typical in homes of at least that era, maybe through the 60's.
It was pretty big, the size of a larger box fan (maybe a bit bigger), and substantial (no plastic). It operated off an electric motor with a belt on it to the fan. It had louvered slats on the ceiling side so it wasn't real noticeable when turned off and the louvers were closed. When you started it up it would pull the air through the house and push it into the attic, which had vents on the gables on either side.
Turn that sucker on and the louvers would open up. If you only had one window open it would make the curtains on that window stand straight out into the house! Small creatures would be sucked onto the window screen...
It was best to open a lot of windows before you turned it on. It was very effective in creating a breeze through the home and cooling it down rapidly. It saved me a bunch of money on A/C bills because I found I could use it effectively in cooling the house on all but the hottest or most humid days.
So yes, they are effective. I don't know if you can find one from an old house somewhere, but if you search on attic fan on CL or something, or call around to demo companies you might be able to some up with one. In your case, with no windows, you'll have to open the garage door a bit to get the breeze to work, but I think it would help.
Here is what I am talking about. They make them in various sizes:
http://www.northerntool.com/shop/to...s&cm_ite=255331?ci_src=14110944&ci_sku=255331