Yesterday I was given my brother's old laptop - core i7, 2.67GHz, 8GB RAM, 128GB SSD, Win7 64 bit. It's a Sony Vaio Z11. Approx 18 months old.

When running something computationally intensive, the fan starts up and after about 30 secs it just powers itself down with no warning. I guess it is overheating. There is nothing in the event logs to suggest what is causing it - the only thing I see is "the last system shutdown was unexpected" or something similar. This is a problem for me because I use a lot of number crunching apps, which pretty much makes it useless to me. I would like to know if there is anything I can do, other than the obvious things I've done already - open up and clean out dust, re-install the OS. According to my brother, this problem started about 6 months ago when it was already outside warranty. If it's just used for simple things - web browsing, word processing etc, the problem does not occur. Any ideas for what I can do to fix this ?

Update: I found that the laptop has 2 hardware settings for graphics: Speed and Stamina - the Speed setting seems to use an nvidia GEforce GT 330M, while the Stamina setting uses an Intel chipset. With the setting on Speed, I can hear the fan the whole time, and the system powers down after a short while (5-10 mins) even just doing basic tasks (browsing this site for example), but doesn't shut down if I just leave it switched on. In this mode it also sometimes just freezes the screen and I have to power off myself. However on Stamina setting it only powers down when doing number crunching and never freezes the screen.