I have two 7970 in an antec 900 case (closed, 5 fans running 100%) and these things are 86c and 97c.
That's with stock settings no overclocking. Yes, they run about 550Mhash each per the spec.
Guess I need to open the box and blast them with a fan or plunge into water cooling...
The temperature is too high for your card.
I use two MSI HD7970 in case SliverStone RV02B-W. Default clock, temperature are 72~75c (Fan 65%) and 68~70c (Fan 55%) (ambient temperature 18~22c).
I took the side of the case off and laid the whole thing on it's side. Temps are now 70s.
Now it's happy.