Vaio Z-590 shuts off while afk, and while using hdmi

It has never happened while I've actually been at the computer using it but at least once a day I'll come back to the VGN-Z590 and it'll be turned off. When I turn it back on I get the option to boot in safe mode, which makes me think that it shut down unexpectedly.

Essentially the same thing will happen while I've got the hdmi cable plugged in and I'm playing a dvd from the laptop to an external TV. In this scenario it happens much more rapidly and predictably. It seems that it can't go even 5 minutes without shutting down when the hdmi port is in use.

I notice that the computer does get quite hot on the bottom of the left side. If I had to guess, I'd say it's overheating when it has to work for the external display. I can't understand why it'd be overheating while I'm afk. I'm obviously more demanding of the system while I'm at the computer than when I'm away so you'd think that if it were going to overheat, it'd happen while I'm sitting there, not in the middle of the night when it's working less, and the room is a bit cooler, etc. And it's not just at night, it could happen in the 30 minutes I run out to grab lunch.

I've taken a look both in Vista and the bios (which is pretty sparse in the feature department) to see if there are any power settings that might be causing the problems. The bios has no power options and Vista's settings looked fine. All as expected. Apart from the hdmi cable issue, the shutting off is unpredictable. Sometimes I get up and check it in the morning and it's still on, other times off.

As an aside, when I've had the laptop hooked up to an external monitor, if I switch users the system will regularly lose its maximum resolution. I'll have to downgrade to 16bit from 32, and/or reduce the resolution to something much less than it's normally capable of. If I set it to what it was before it forced a reduction on itself, it won't accept the settings and it'll revert to worst possible settings.

Any ideas would be appreciated. Fortunately I'm still within a year and under manufacturer warranty. I've already ordered my box from sony to send it in but I figured I'd pick your brains before I do that just in case there is something I'm possibly overlooking.