i didn't say gtx 580 i said gtx 570. and depending on where you're buying from, on newegg anyway, a gtx 570 can be found for $50 less than a gtx 480. it performs basically the same, it runs cooler, consumes less power and is cheaper, don't see why you would still get a 480.
if your pc is setup like that pic then no it won't fit. the hdd closest to the bottom of the case would be directly in the way of the card.
here's another pic of your model
Imageshack - img2359mo5.jpg
you see that it'll be a snug fit even when you remove the bottom hdd.
and for additional cooling, i can't really tell if that case comes with a fan in the front or not. if it doesn't, i would just buy the biggest case fan that you can fit in there an just rig it with zip ties or something just to get some kind of airflow in there.