The GTS 250 is about on part with the 8800 GTS 512MB video card and the 9800GTX (because they're all the same chip basically).
Mirror's Edge is not a great game for testing that video card. PhysX will destroy that video card when playing Mirror's Edge. Turn off PhysX and it'll perform a LOT better. All PhysX really does in that game is allow you to see glass particles when glass explodes. It wasn't that big of a deal for me.
As for 1650x1080, the GTS 250 should do fine for you over all. However, with more recent game titles you're not going to play at all high settings. Medium to High settings would be the way to go, with certain things like AA and Shadows turned down.
If your CPU is already running that hot I wouldn't overclock. Getting a decent cooler for the CPU and/or adding a fan or two to your case is a decent idea though.
A GTS 250 isn't great for 1680x1050 but it's respectable. It really should handle COD4 at the very least;
Might be an overheating CPU throttling down to lower speeds so it doesn't kill itself. I'd start with your high CPU temps and work your way up from there. Keep in mind due to your lower GPU memory amount your speeds should be more then the 9800GT, but just under the GTS250. If you see a 9800GTX+ listed thats your card.