The exact same thing happens to me on my windows vista computer. I've been in SL sense about March 2010 and in about January of 2011 I would turn SL on and login and i would play for about ten minutes and my entire computer shuts down. I found a way to keep SL running for a little longer, dont stay on the SL page too long, go to the internet like every five minutes like the marketplace or something. But I dont think its heat cuz i have air conditioning blasting in my house and fans next to my desk pointed toward me and the computer. So I dont really know. I've done countless scans and stuff and its not helping. :-(