So I finally got around to doing this upgrade. The parts came a long time ago, but I got busy with other things, and it seemed like maybe the T9600 upgrade wasn't a good idea for a machine that already ran a little on the hot side.
Well, the T9600 and the new fan are installed, and the machine runs much cooler. Found the culprit: https://flic.kr/p/G6Yqhd
I guess you were right, jaspen-meyer. You don't need a fan. Mine couldn't have been accomplishing anything.
Anyways, right now my cores are running at 36C and 39C, which is at least 15C lower than before.
Edit: I just watched some Youtube, and the cores fluctuated between 40C and 42C. Tasks that used to drive my CPU usage to 50% are now only putting it into the 30-35% range. I'm quite pleased.
Edit 2: Well, I must not have seated the CPU correctly (or I have a different loose or damaged connector somewhere). If set the notebook down (I think bumping it from the bottom is the issue), it freezes. Back into the guts of the thing I go!
Edit 3: Rookie mistake. I thought the CPU lock screw turned 90 degrees, but it turns all the way around to 180 degrees.