Linux shuts down randomly

I have an older Arch system (fully updated though, just older hardware). A couple of days ago during the night it suddenly went into a reboot loop, rebooted several times then turned off. I know because I happened to be nearby when the fans started blowing on boot. That kind of behavior made me think maybe it was a thermal issue.

The next day I brought it back up (after a well-deserved anti-dust treatment) and could find nothing wrong with it, except that somewhere in the middle of the night, logind received an ACPI short power button press and shut down.

Not being defeated that easily I disabled logind's related action.

Just now I've been away for 5 hours I come back and it's still physically powered on but no longer functional (display insists there's no signal). In the journald log there's a series of Power Button pressed events (at random few-second intervals over the course of about 6 minutes) multiple hours ago, then nothing. Again while I was away. And even though logind is taking no action there are no other log entries, as if all background processes immediately stopped working. But no more shutdown messages in the log either, the button press events were the final messages:

Sep 09 17:57:28 itxnas systemd-logind[1431]: Power key pressed short.
Sep 09 17:57:50 itxnas systemd-logind[1431]: Power key pressed short.
Sep 09 17:58:52 itxnas systemd-logind[1431]: Power key pressed short.
Sep 09 17:59:19 itxnas systemd-logind[1431]: Power key pressed short.
Sep 09 17:59:21 itxnas systemd-logind[1431]: Power key pressed short.

Sep 09 18:01:52 itxnas systemd-logind[1431]: Power key pressed short.
Sep 09 18:02:39 itxnas systemd-logind[1431]: Power key pressed short.
Sep 09 18:02:45 itxnas systemd-logind[1431]: Power key pressed short.
Sep 09 18:03:03 itxnas systemd-logind[1431]: Power key pressed short.
Sep 09 18:03:03 itxnas systemd-logind[1431]: Power key pressed short.
-- Boot 83f3f4b1c5214cd494bdc3a2c9c6b733 --

I'm curious. System is still on so it did not shut down from thermal issues. Also, it only seems to happen during inactivity thus far. What should I try next?

Can it be a power button wire short? If so, a short press should not cause a hardware response, just an ACPI one, right? And a 4-second press causes hard power off. Since it is still on and responds to CTRL+ALT+DEL that didn't happen. Hmm... maybe there's a BIOS setting forcing it to power back on? But that's only on power failure, not power button.

Can it still be thermal issues? Maybe somebody could tell me how to set up a script to log temperatures to a file so I can see if it starts getting hot all of the sudden.

It would make so much more sense if it happened at random times, not just 3 times in a row while I was AFK.

EDIT: Well, it's not inactivity, it just went while I had a watch active through an SSH session and it was on my display. Display showed nothing, just went black and then booted. It sits in the boot for a while, then reboots again, even physically turning off and on. Must be a short then.

For no useful purpose at all (except it looked cool) I did order a little standalone power button from Ali a long time ago. Guess it was useful after all. I plugged it in, system is running again now. Now to find out if it happens again. Then it's either thermal or motherboard?

The case also has a reset button but it looks like that wasn't plugged in, just the power switch and LED.

I really hope this is it, some of the apps running on this thing are not easy to migrate and storage for a replacement system to do live migration costs about as much as surgery.

EDIT 2: I did a crude watch --interval 5 sensors on an SSH session. If it does happen again the last reading should stay on the screen. All readings are perfectly normal so far, except AUXTIN which scares the heck out of me but is a faulty reading.