This shut down is due to your system overheating because the cooling system i.e. the heatsink radiator and cooling fan is caked with dust particles.I Have a PCG-GRZ570 which had the same problem and was rectified by a good clean-out - it now works like the first day i got it.
The shutdown is a safety shut feature when yr machine gets to an unstable temperature and will cause damge to surounding chips if not rectified.The memory sockets are also known to give in, due to this heat build up, resulting in the machine failing to boot up.
To clean the system out you need to strip the laptop, and remove the fan housing, cpu, and heatsink.This must be done rather than using compressed air to blow out the dust.
If you need more information on how to do this, let me know.