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it depends on what you put in the inside and how do you clock it, then from the room temp.
Maybe 2-3 cards underclocked and undervolted in a fresh room could be ok.

On default settings of memory and voltage I think they will get hot in a short time if you keep the case closed.
And if you have to mine Litecoins the problem gets much hotter.

a good case flows air better than an open air scenario, but the problem is spacing the GPUs apart which becomes an issue when you use more than two cards as most are double slot cards and if theyre stack right next to each other they will get hot

I run 8x5870s in two XClio Windtunnel cases with all fan slots filled.  I used pcie extenders to space the cards out; this required some creative mounting and motherboard choice is critical.  Also, I have a 100w exhaust fan pulling fresh air into the room.  Undervolt in the summer/daytime, overclock in the winter/nighttime.

I also have an open air setup with 3 5870s, and they run a little cooler.  I've had to replace all the fans once due to dust, both on the cased cards and the open air cards.

I would say as long as the 7950s are dumping exhaust mainly out through the back of the case, and there's a path for it to get away from the case intake fans, it should be OK. 

Too bad GPU mining has a finite lifespan these days... at least when it's over you'll have a ridiculously powerful 3d/multiscreen gaming rig to play with.

A proper push/pull large (120mm) fan configuration back to front in an enclosed case should cool better than just letting them sit out in the open I would think. Depends on the environment they are in too though, cool spaces away from your living area are best naturally. If you live in a cold place your mining rig can double as a space heater that pays for itself  8)

I just got my 7970's yesterday. Not done extensive testing yet but opening the case increased temperatures by 5 degrees so the case is now closed.

This matches with my experience working with high end servers.

The only way I imagine open air cases working is if you stick a massive room fan to it.

An open air setup with the 1 card plugged directly in the first slot and the rest of the cards on extenders and arranged in staggered position (@ 130 - 140 degree angle) is about 10 degrees cooler than any closed case setup I've used in the past.  

If I had more time and/or was more enterprising I would design the 180 degree (angle not temp  ;)) setup that's in my mind.  Basically each card installed flat on platform above MB and fans blowing to the sky... I never understood the card separated by clothespins or blowing hot air into to each other setup. Except for space limitations I suppose in huge setups.
  

As far as enclosed in a case, my cards have been running all day, first 12 hours of mining! 68c, 71c, 78c. Which is because the 3rd one is really close to the bottom of the case.

Ambient temps, 22c at the front of the case, 23.5c at the back of the case. I've got a 5400rpm 120mm fan at the back doing the extraction, and another at the front of the case which is blowing cool air directly down the channel of graphics cards. I've pulled em down to 4000rpm at the back and 3500rpm at the front. These are serious server type fans.... So lots of airflow.

Ambient temperature in my room is 24 degrees, it doesn't ever get very high as I live in an old brick house so the summer's are still cool.