This really does sounds like an overheating problem, MAYBE. Why I say "maybe" is just as rdslw said above: normally if your CPU overheats, you get an initial slow-down of performance, and if it gets too high, you get a warning before any shut-down. Overheating of an added graphics card (you may not have, not in your list) MIGHT cause the graphics card to shut down and leave the rest running.
There's another possibility that can cause a very rapid shut-down. The CPU_FAN header has an important second function: it monitors the speed signal of the CPU_FAN cooler (or whatever is plugged in there) for NO signal (or in some cases, a speed lower than some limit). If that goes into the low speed area, it interprets that as a FAILURE of the CPU cooling system, and that can cause major damage quickly, so it puts out an immediate warning. On many mobos (but not all) it does much more: it actually shuts down your entire system very quickly without ever waiting for the temperature sensor inside the CPU chip to indicate an excessively high temp. Some such systems also will not allow you to re-start until the fan DOES indicate proper operation. IF that is what is happening, there are two possible causes. The obvious one is that your CPU cooling fan actually DOES stop for come reason - either it is failing and seizes up, or your fan control system it telling it to run too slow, and it stalls and fails to re-start. The other is less obvious - there may be a bad connection where the fan connector plugs into the CPU_FAN header, and from time to time the speed signal from the fan does not get to the header pins.
To start, watch your CPU fan speed and the CPU temperature. That can be done in BIOS Setup, but not while you are working. Instead, you should have a fan and cooling monitoring utility called SmartFan 5 on a CD that came with your mobo. It may already be installed on your machine. Find that and just run it under Windows as an app. It has several screens of info so you can observe while doing normal work. Keep checking for what the CPU temperature is, and what the fan speed is, especially the CPU Fan speed. If the CPU TEMP keeps going up and up too high before it shuts down, you do have a genuine cooling problem. If it stays under proper control but your fan speed gets very slow, OR stops entirely, you have a fan problem. Could be either of the items I cited above. IF the fan speed goes really slow (can't tell you what is too slow because I don't know what cooling system you have), it just might be on the edge of stalling. If the fan speed seems normal and relatively stable, watch for any indication that it just suddenly stops before the crash. That MIGHT indicate a real fan stall, or it might indicate that the fan kept running but the speed signal failed to get through.
IF you suspect the fan is being told to run too slow, look in your mobo manual on p. 25. There is a configuration option for the CPU_FAN header called Fan Stop. You are allowed to let the fan stop for some fans, but this option (IF it exists for that CPU fan) should always be DISabled so the fan control system can NOT tell the fan to stop. Note also that this option includes an ability to specify exactly what low temperature is used to trigger stopping the fan.
If you suspect the fan signal randomly fails to get through, there may be a and connection for Pin #3 at the CPU_FAN header. That can happen from loose connection or just from oxidation of the contacts in the connector. The easiest way to try to fix that is this. Shut down your system. Open the case. Carefully unplug the CPU cooling fan connector from the CPU_FAN header, then pug it back in. Repeat several times. When finished, ensure it it plugged in securely, close up the case, and start up normally. Keep monitoring as above for other clues. What this action can do is gently "scrub" the surfaces of the connector contacts and the mobo header pins to clean them and re-establish a good connection.