I have two 7970's - one GHz edition and one normal edition. Running them both on high I have no issue keeping temps under 80 degrees. I would highly recommend you look at getting some more airflow into your case. I actually modded my Bitfenix Shenobi to allow me to mount a 23cm fan directly blowing air onto the cards.
+1
I also Have one of each, they need light airflow or yes they overheat. I have a 180mm AP182, excellent fan and overkill but works well.