7 x 5970's would give you just under 35 Teraflops instead of 12.
8 5870s packed into two cases would survive if you keep the cases closed and put 3 Delta AFB1212s in the front pushing all the air through the cards and out their rear vents, this is how most Bitcoin miners build cases.*
If done right, 8 5870s should easily be kept under 85c even when marginally overclocked.
* Large scale Bitcoin miners have a habit of not using cases and use flexible risers to keep the cards away from each other out in the open. I do not recommend this as you lose out on high pressure cooling, a staple of enterprise/high performace computing.
Before adding water cooling - it would lock after 30 minutes of mining at standard 725 Mhz.
This system worked very well for ~4 months (and then I sold it to guy from Alaska, since it became too hot in Texas :))
(http://fastra2.ua.ac.be/?page_id=53)
They claim "slightly over 60 degrees".