A Core i5-2500K will cost you $220, $120 can get you a decent P67 chipset motherboard and all you need to do is add in another $50 - $70 for some decent 8GB of RAM. That would outperform the Q9650 by a long shot. Not even a contest.
If your goal is to have a fast system, jaguarskx nailed it -- you can't realistically get close to the performance of an i5 Sandy Bridge setup, for about the price of maxing out your s775.
If, however, you just want to fix your rig on the cheap with a CPU that isn't committing suicide by overheating, you can just pickup something lower in the food-chain (say a dual-core Wolfdale) for under $100 -- just make sure your mobo/bios version support the chip you buy.
Keep in mind that your CPU may be overheating due to a Mobo issue, so you may just be buying yourself a spare cpu and end up replacing your mobo anyway... You may want to borrow another s775 CPU from someone and verify that it can run at reasonable temps before you drop cash on a new CPU. If it's a bad mobo, you can replace a s775 mobo for cheap, or upgrade via jaguarskx's suggestion...
I just recalled that a friend of mine had this exact problem. In his case, it turned out that he'd recently flashed his bios, and the new version defaulted thermal shutdown to something needlessly low, like 70C... So, you may want to check your bios and make sure it's not choking your machine well before your CPU's real threshold.