Why Am I Running So HOT?

All good things to think about.

I'm not overclocking.

And I'm very happy with the new ZALMAN CNPS7000-Cu heatsink I put on there.

As for the thermal paste, I just used the stuff that came with the heatsink.
I know that the best stuff is called Arctic...something...but I got cheap and just went with what I had.

My case is under my desk...I could probably cool things down another touch by putting it on top of the desk, but then I would have to discuss aesthetics with my wife and that's just not a hill I'm going to die on when things are running perfectly fine right now (with my computer AND my marriage).

It's a bit "after the fact", but here's my two cents anyway. Use it as you please.

The problem you describe where a game shuts down is typically a graphics problem. Usually if the CPU overheats the whole system will shut down, not just a single application. And it's not necessarily a heating problem. It can be anything from outdated (graphics) drivers to a faulty card. It's difficult to pinpoint a problem with a graphics card. If updating drivers (including directx) and making sure the graphics card's fan is working fine does not solve it, the solution is unfortunately usually to buy a new card.

Similar problems caused by other cards were resolved by setting the AGP speed from 4x (for instance) to 2x.

Another source of the problem could be that your PSU (Power supply) isn't pumping out enough power, the graphics card can't perform properly and it "shuts down". You can lower the DPI to make the power usage a bit less... You can compare your PSU's output with what it should be using tools like these:

Power Supply Calculator

Yes, if you have a brand new GPU, say a 7800GTX...nVidia clone or branded...you need a 600W+ power supply or else your system will be drained. Even though 500W is OK, all of your other hardware and trinkets you might have will drain that power and as soon as your GPU needs more power to pump out massive graphics, it will shut your system down...like when you blow a fuse or trip a breaker.

This is also after the fact, but what was the exact error condition that you were getting? What did the message say?

Anyway, it sounds like you did the right thing by replacing the thermal compound. The reason it dried out in the first place was probably due to old age, dust, and a hot-running card such as graphics.