Previous shutdown cause 0 on Mac Pro 2008

'Previous shutdown cause 0' would appear to be 'power disconnected', from grg's Shutdown Causes.

I would have assumed this would only apply to laptops if they ran low on battery, or a desktop if there had been a power cut.
Standard indicators of an actual power cut - flashing kitchen clocks or other computers rebooted, there is no sign.

However, I've noticed my sleeping Mac Pro 3,1 has rebooted mysteriously with this cause twice this week. I heard it boot at 7.13 this morning & after investigation found another similar even from 4am two days prior to that.

This machine is used as a media player & so really the only thing running is VLC. The indicator, if I don't hear it start up is that VLC's playlist is empty - so I can pretty safely say it's only ever done this twice, as I rely on the playlist knowing where it is every evening when we sit down to watch TV. It's the kind of thing you notice if it's empty.

From previous questions, pmset details as follows [I'm currently remoted into it, preventing sleep]

pmset -g
Active Profiles:
AC Power        -1*
Currently in use:
 hibernatemode        3
 womp                 1
 networkoversleep     0
 sleep                30 (sleep prevented by screensharingd)
 Sleep On Power Button 0
 ttyskeepawake        1
 hibernatefile        /var/vm/sleepimage
 autorestart          0
 disksleep            10
 displaysleep         30

OS is 10.11.6
I've reset the SMC, just in case, & run AHT, short & long tests, no errors. I would be keen to hear if anyone has any other ideas as to how to go about diagnosing this.

Considering it is an eleven year old machine, I can quite safely say (from three decades as a hardware tech) that either the power supply is starting to play up, or one of the voltage-regulator blocks that keep its Xeon(s) well fed are starting to get constipated with age. Either scenariou is equally plausble.

When was the last time the ol' cheesegrater had a full strip-down, clean (which includes taking the cover off the PSU, they make excellent dust filters!) and some fresh thermal re-paste?