HP DV7-1270us :: Game Lag / Overheating And Shutdown

My problem is with over-heating, I've had this laptop for a while, and although I've maintained it, It has been used a lot. I've installed a few games, and while playing them it's not uncommon for the laptop to overheat and shut down. The laptop normally gets pretty hot, when it's on for extended periods of time (but doesn't usually shut down), the fan does work, and does go faster when the laptop's doing a lot of things.
 
My issue with this is, let's say for example I'm playing GTA IV; this laptop is equipped to play this game, based on the minimum recommended hardware, and also the recommended (besides CPU) so I would naturally assume playing it is going to be with no lag, or problems. This is not the case as with other newer games, Mafia II, Dead Island, and others gave me the same problem, starting them up and playing usually gives me good FPS (playable anyway) but after maybe ten minutes, very rough lag starts, I'd get like a maximum of 10FPS if even that, despite the fact I know my system can handle it.
 
So far I've
- Open the laptop, cleaned it out, ensuring no dust is in it
- Defragmented the entire C drive, had over 50k fragments
- I use gamebooster software when playing games to ensure no resources are wasted on background programs
- Tweaked my nvidia geforce 3D settings to maximize performance
- Tweaked settings in game, low graphics, etc
- Updated Graphics card drivers to latest version
 
All of this maybe got me a few extra FPS, so you can see my frustrations, I've exhausted every option I know, which is why I've come here, the lag problems seem to be related to the overheating problem because like I said booting up the games from a cool laptop, usually means playable FPS, but lag starts as the laptop heats up, and uses 100% cpu power. My only other thought would be replacing the thermal paste. This is a pretty strenuous operation.
 
My specs are:CPU: You Have: Intel(R) Core(TM)2 Duo CPU P8600 @ 2.40GHz
CPU Speed: You Have: 2.4 GHz Performance Rated at: 27.048 GHzRAM: 4.0GBOS: Windows Vista Home Premium SP2Video Card:GeForce 9600m GT300GB harddrive, 107GB free right now, direct x version 11