I'm not familiar with those 7970s, but if they are voltage locked, might be difficult to keep them from overheating inside a case. Open air setup would be better.

BTW, I have three 7950s inside a HAF X and they run cool enough, but I don't know about three 7970s... If you go with the HAF X, be sure to remove all the dust filters from under the various grills to improve airflow. There's enough room inside that case to rig up risers to get even more separation between the gpus. Also, for my Sapphire 7950s, I found them to run cooler if I reversed the side case fan to make it exhaust instead of intake.