6970s run very hot, a friend of mine has one, it puts out a ton of heat. It's really fast though
Mine runs warm for me, but not any hotter than it ought to. Certainly cooler than the previous two generations; the 48xx cards were very hot (even within design specs) and the 5870 wasn't the coolest either. I haven't had Deijya's issues, but it may depend on when we bought our XFX cards and which model we purchased; mine is an AMD reference design, and those differ from later rev. 2 designs from vendors.
For the OP's system though, I think a 6950 is a better card, the 6970 will probably be CPU limited (I'm assuming that's a dual-core Extreme, not a quad). You can get the 6950 for as much as $100 less (depending on whether you go 1GB or 2GB of RAM).
Core i7-2600K @4.2GHz, GIGABYTE GA-Z68XP-UD5, 4x4GB G.Skill RipJaws PC1866
Corsair 650D case, Seasonic X750 Gold PSU
WD `Raptor 600GB boot, WD Caviar Black 1TB data, NEC 7200 DVDRW
2x Radeon 6970 2GB in Crossfire, X-Fi Titanium, Dell 2407WFP