Well that theory was shot down in flames the night before last, as I got 3 shut downs in one night. The repeated shut downs would make me consider an overheating problem if it weren't for the fact that it's never presented like that before. Previously after shut-downs it has started up again very happily after and run fine. (And even on this occasion, we're talking 20 mins or more between them.)
I have replaced the extension cord with others I had to hand, as a quick and easy experiment.
I am not ignoring the advice to do a memtest - just got to find the time to get around to doing it.
I'll keep reporting back, in case the results of this thread turn out to be of any use to another.