It could definitly be a bad power supply, they will go out intermittantly from time to time, but there are a few things we can do to narrow that down a bit. It could also be ram if you have a significant amount and aren't hitting that ram register very often. Or a short in your reboot jumper or switch on the board. Do you have any pets that might inadvertantly hit the reset switch?
First things first, your 25c (77f) temperature is really, really low for most of the components in a computer. to the point where I don't know if you are getting an accurate read. Download and install the free program Speedfan (http://www.almico.com/speedfan.php)
and report what those temperatures show at idle for any of the components that can be monitored. Also check the hard drive S.M.A.R.T. error section while you are in there for any issues with the hard drive, just to rule that out.
Depending on the motherboard model you purchased, there may be a power monitoring module built into the bios. All asus motherboards have one, most other manifacturers do. You can check the temperatures direct from the bios level at that point, but more importantly, the power supply voltages the motherboard is recieving. The main important ones to use as a diagnostic for the power supply will be the 3.3v, the 5v and 12v voltage inputs. Your motherboard can correct and compensate for any differences +/- .5ish without too much issue, depending on the reference design. Most power supplies won't deliver the exact expected reference voltage. Thats what you pay many dollars extra for an enermax PSU for. but most of them will get fairly close. those numbers will tend to vary a bit as supplied electricity to your computer varies as things in the house turn on and off, or power compay delivery dluctuates a bit, so a bit of up or down drift .2 +/- is expected, maybe a bit more depending on your PSU. If any of those voltages are significantly off, or if they are wildly fluctuating, even intermittantly, then you might have a bad PSU or a bad voltage regulator on the motherboard (usually caused by partially cooked capacitors). If those are stable throughout, its probably not the PSU.
If the PSU checks out, i'd suspect ram. especially if you have all the ram slots filled. Oftentimes core 2 and core i7 era motherboards will require an updated bios on the motherboard to fully support a fully loaded ram setup. I'd check for and apply a bios update first before trying anything else. If that all checks out, download and burn the memtest disk (http://www.memtest86.com/download.html)
and let it run through a few test cycles and see if any of your ram slots are showing signs of persistant errors. You'll want to let it run at least a few hours to simulate full gaming load. Any sticks that look iffy, take out your other ram sticks and move the iffy one to the primary slot. it will either work right, or fail miserably at next boot. If it works, try all the others, rinse repeat, etc. In the bad ram scenario that would force a reboot without bluescreen, it would have to be one of the sticks in the secondary slots of the last channel, that aren't being accessed on a regular basis.
If it isn't the PSU and it isn't the ram, it could be a bad motherboard capacitor. There will usually be physical evidence of that in the capacitors around the CPU mounting area. In that scenario, the PSU powers up the computer fine, the processor runs through its cycles fine, and cycles through the capacitor discharge cycles as normal, but ocasionally after the machine has been on a while, the damaged capacitor looses the ability to fire correctly, or begins to hold less of a charge than required. If this were the case, you would usually see this show up more during heavy use.
CPU failure would be a no boot, ever issue. they don't partially fail anymore very often. You can try swapping it out anyways if you have a spare.
Chassis wiring with stripped insulation could also theoretically do the trick, especially if its a power lead or the reset switch itself. You might want to try unplugging the reset switch entirely if it is wired and see if that fixes the issue, though that would be unlikely. Do you have a motherboard test stand? if not, and if you are building computers fairly often, you can make a decent one out of a large melamine plastic cutting board, drill some holes, thread some nylon screws through with some plastic washers the size of brass standoffs in the corners and at a few places to support the board, etc., make a fan bracket to power a fan to blow air over the board, you get the idea. then you can electrically isolate it and test it with a known good power supply outside the case.
Hopefully that gives you a few places to look at least.