2nd graphics card is running hot while the other is fairly cool?

you could crank up the fan on the hot card.

try this |MG| EVGA Precision 2.0.1 Download

Exactly what I was going to recommend myself. Either crank the fan up or exchange the card locations and see if the card runs hot when you swap it for the top slot.

Can you check the load balance on those cards? If the second card is under a heavy load while the first card is not you could have your answer.

What exactly is hot? To the touch or gauged by an application that displays the actual temp.

And I highly doubt the power supply or slot are causing this issue. More likely you need better cooling by adjusting the fan or changing the card locations to make air flow better.
 

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At a glance

Win7 64bit UltimateAMD Phenom II X6 1100T Black Edition Thuban 3...CORSAIR DOMINATOR GT 8GB (2 x 4GB) 1866 DDR3XFX HD-697A-CNDC Radeon HD6970 2GB 256-bit
Computer Manufacturer/Model Number
Custom
OS
Win7 64bit Ultimate
CPU
AMD Phenom II X6 1100T Black Edition Thuban 3.3GHz, 3.7GHz
Motherboard
Gigabyte GA-890FXA-UD5
Memory
CORSAIR DOMINATOR GT 8GB (2 x 4GB) 1866 DDR3
Graphics Card(s)
XFX HD-697A-CNDC Radeon HD6970 2GB 256-bit
Sound Card
Creative SoundBlaster X-Fi Platinum Fatal1ty Edition
Monitor(s) Displays
Dual 25 Inch Hanns-G HZ251
Screen Resolution
1920x1080 X 2
PSU
Corsair 850W Single Rail
Case
Thermaltake V9 BlacX w/ Dual HDD Docking Station
Cooling
Air lots and lots of air and copper...
Keyboard
Kensington (Low-Profile)
Mouse
Creative Fatal1ty
Internet Speed
15Gbit (15 Down 5 Up)
Other Info
XIGMATEK HDT-S1284F 120mm HYPRO Bearing CPU Cooler, LG Blu-Ray Burner.
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