From my experience, spontaneous reboots with no BSOD don't leave error codes anywhere. It's analogous to simply unplugging the computer.
Also, from experience these types of spontaneous reboots are almost always related to CPU or RAM, but in various ways.
(1) Bad stick of memory or bad RAM slot on motherboard: least likely IMO because RAM errors often generate a BSOD, not a spontaneous reboot, but it can happen.
(2) Heat. This would be my first guess. Remove the CPU heatsink, scrape off any thermal compound on the heatsink and clean it with alcohol, reapply thermal compound and reseat the heatsink. If you don't have thermal compound laying around, you can get some from RadioShack that works well enough.
(3) Overclocked/overstressed CPU or system. A CPU or FSB pushed too far will cause spontaneous reboots like described above. However, this usually happens during stressful applications, not randomly or while checking mail. Sometimes an overclocked CPU can generate enough heat to reboot randomly, and this is fixed as described in possibility (2). However, from the general computer experience of Anon_me it's pretty safe to assume that this system is running stock. In that case, if the CPU is unstable it is being caused by poor cooling (see (2)) or by low voltage. Which leads us to...
(4) Inadequate powersupply. A PSU that can't maintain voltage, or has poor filtering, can cause spontaneous reboots, as it effectively makes the CPU mimmick under stock conditions one which has been overclocked (i.e., the voltage is too low for the frequency being ran). This would be my second guess as to what the problem is.
You can likely narrow the problem down to the most likely culprit if the system is not new. In other words, if you've had this system for a while and it only recently started this behavior. In that case, it's unlikely to be possibility (4) since PSU's have a very low failure rate. Look to overheating (2) to be the cause and course of action to correct it. If the system is new, then it could be either heat or PSU. I'dd address the heat issue first and see if that corrects it, if not... tackle the PSU.