I'm having this problem also. Not heat related for me. I have never had a heat related problem with this computer ever. When it shuts down during a LR import, it does so in a controlled, intentional manner. The screen fades out gently, then it takes a moment to do its thing before the computer actually turns off. It's not like it just shuts off suddenly like it lost power or something.
It usually does this during the middle of an import. It doesn't do it every time, i'm not sure of any particular circumstances that cause it, and i cannot recreate it.
I'm running an HP DV2500t series laptop with a bunch of usb peripherals (keyboard, mouse, external drive, external cardreaders, etc) and a Dell external monitor. The lid to the laptop is closed. It's never shut down on me like that in any other software, only Lightroom. I'm using LR 2.3 but am currently downloading an update.