Opened case? Fan going and you have the side off? Gets hotter in there with any side off the case at all. Think it would be cooler but actually not designed to work that way.
Anyway, thought I'd reply since I was have RAM problems and almost like yours. Didn't matter 20min to 1 hr, would just shut off and had to let is rest before booting it back up. Waiting for replacment RAM now, way slower than what went defunk. Give this a shot, get into BIOS and change the CPU speed down one or two notches.
My CPU can run 2100MHz but since of the RAM error down to 1440MHz, double check that RAM in every single way possible, wear that strap too.
If that isn't it and still can't get her going, test the power supply under load, handy dany multimeter and paper clip the green wire to black, then check your voltages, lots of sites on that.
Sum up everything I just said, put the side panel on if it is off, will get into CPU errors from heat. Check your memory, every which way and then your power supply. Just changed it, so more than likely not it but have a feeling it is the RAM, wouldn't be anything else that I can think of or just come down to a few of those problems.