This model Sony has overheating problems. I solved mine by making sure heatsink is clean, plus I dissembled and cleaned the CPU and heatsink. Then reassembled using some high-quality Artic Silver thermal compound betwixt the CPU and heatsink. Runs Win7 very nicely now!
Have also run Debian 5.0.2 "Lenny" on this with much success. It never ran WinXP very well for some reason - could be because of overheating although I never had the shut-down issues you describe. Most owners of this model do have those same shut-off issues.
If you rip your keyboard out and use an external one, you could mount a proper desktop sized heatsink/fan on the CPU (it's just under the RH speaker near power button).
That would solve this issue permantly at the cost of "reduced mobility" - LOL
Cadstar
September 2009