I'm also thinking that 3 7970 will have some heat issues without risers in that case. Generally closed cases are a bad idea.
Pretty much this. That case is tiny, and beyond that the cards you've chosen don't expel the hot air out of the case, but just circulate inside the case. Seeing as how you haven't built this, and just compiled the parts I can see how it would be easily overlooked. But I can guarantee that you will have serious overheating problems with those cards. If anything I'd switch to reference designed cards, so at the very least a majority of the hot air will be pushed out by the card fans. Even then I wouldn't expect to be able to overclock much and maintain safe temps.
Okay, thanks for the input, ill look into that. I was talking to one of my friends on this forum, and he said that it shouldn't be too much of a problem, except for with the middle card, since it will be pulling in the exhaust from the far card. I will also be adding an extra fan to that case, in increase air-flow as well... Do you agree?
I foresee the card temps to be about 90c+ inside that case, a fan won't help much. They need open air and plenty of space between cards. No one runs a mining rig 24/7 with a closed case (or any case for that matter).