Hi G
Did you re-examine the BIOS ?
If it has a "suspend to" feature OR "what behaviour if power is interupted"
(by power Co. failure or accidental button hit )
- which computer will not know
how it was powered down_
If state has been inadvertantly set (ON) >
restarts when/if power is available:
The BIOS is doing exactly as it should (reboots)
If no other oddities were noticed -
& Esp if anyone accessed BIOS - the settings are easily missed.
Another possibility - the physical "reset" on some non-laptop computers
There is an Mfgr's sometimes lengthy delay - same as any automated circuit breaker
Punching (literally) that same buttom, re-cycles power events
Much as when resetting a circuit breaker too soon
BTW - memtest will endlessly access/loop
same RAM bank portions -
in same sequence !
Three or four loops will suffice for it
What is wanted - the stress of
random access
IF an errant flag is

not re-setting -
it may even be the
pointer flag that indicates if energy is stored (in use)
or now re-usable to "writes" (MT)
"Dirty" flags are indication of degrading RAM
If/when memory seem the culprit:
Try
1st swapping slots
Chances are excellent that combo of accessing will never get repeated.
Even if Ram is deteriorating
Faulty ram will rear ugly head in many wierd behaviour errors
Repetitive parsing, sector read errors - anybodies guess
The thing to note > it will be more noticeable the more the RAM
gets stressed (Linux accesses in flat/linear mode)
Some have found - using (Linux) md5 against
large as possible stored data
where the data is copied into mem then de-compressed to read/write
& every single byte is checked : Is the more reliable method
The process should hickup at relatively the same task
Best of luck -'tis likely sum -thing simple
(heat factor been considered ?)