First thing I thought was PS too!

I had put together a PC for a friend, using the parts he bought from a store, which was exactly the same as my specs, except for the case and PSU, where he went for a cheaper generic, and I opted for an Antec case with Antec PSU.. his was rated 'more powerful' than my Antec, and was much cheaper($50 against $200).
his was turning off at random moments, and he went through the re-install process and was getting frustrated, until he gave it to me to figure out.
I had it sitting one day at the BIOS trying to figure out a few things, and as it sat there for a few minutes the BIOS page I was on showed that there was a Power failed condition .. ie. the PSU wasn't powerful(stable) enough after a few months of use to maintain accurate voltage levels.
He eventually changed it for the same Antec PSU and the rest is history.

So... this may be easy to trace if the BIOS has a diagnostic page for the PSU.

Would you reckon it may be affected by ambient air temps?

Also! a few more than 3 years ago, some Gigabyte mainboards had faulty capacitors that swelled up(obviously, so you could easily pick them out, which caused random shut downs too)

I had one(damn can't remember the model number now as the ex took it!.. something like a 7VRX??) anyhow finding replacement capacitors was the hard part, and removing the old ones was almost as difficult.
But once I'd fitted the new ones, the issue was resolved(cost about $20 but I got a few spares, just in case)