from my experience with random reboots, there are a few factors to look at:
1) corrupt memory
2) corrupt hard drive
3) heat
4) viruses
i highly doubt viruses are causing this, and you already ruled out heat. more often than not, it ends up being due to corrupt memory. there's a few ways to check if its corrupt or not, the simplest being memtest. download the memtest software. it's free, so don't worry. have it do a quick check. if you start seeing any errors whatsoever, that means it's the memory that's causing you problems. easiest solution == buy some new memory. it's cheap these days, thank god. G.skill 2x 1 gig sticks 65.00 on newegg.com and free shipping if i'm not mistaken.
if thats not the case, look into the hard drive. do a disk check and try it on another computer to see if it's running ok. if not, 50 bucks for a 160 gig hard drive from western digital off newegg.com.
from there, if neither of those are causing your problems, DOUBLE check the heat. make sure that your temp readings are accurate and that there aren't any broken fans, dust, or anything else contributing to heat buildup. try opening the case and pointing a room fan in there just to make sure heat is definitely not it.
if all that fails, i'm not sure what to tell you because i've only ever had experience working with shutdowns due to the causes i just outlined.
keep us posted.