Umm - here are the fruits of my labours but I can't guarantee coherence!
While I was working on your suggestions the CPU varied between 28 and 32ºC, the motherboard from 28 to 34ºC and the HDD was more constant at 42ºC. This was pretty light work and the temperatures were distinctly lower that the totally valid temperatures that I reported above but at least it suggests that the temperatures aren't constantly a little on the high side. I didn't attempt to provoke anything in the way that you suggested at the end of your post..
My malware check, which is done as part of the regular "once-over" at least once a week, was limited to a Malwarebytes scan but came up clear. I don't remember anything being discovered on this computer by Malwarebytes except on its first ever run in early 2007.
Chkdsk showed a remarkable lack of issues. I was surprised.
In the event log there were 3800 notifications, none classed as critical - only errors and advisories, over the last 12 months. The vast majority (although I have to confess to only looking at what I hoped would be a representative sample) were regular repeats which were mainly about printer issues or "RapportKELL" (banking security?). However the last one, about 20 minutes before the computer went into its biggest freeze was an "App crash - GoogleSyncDoc". I didn't have the timings of the other fairly recent crashes from which the machine eventually recovered on its own because I wasn't there when they happened so didn't even try to correlate those with the event logs (by this time it was after 6 am. and the sun was coming up!).
You suggested doing without MozyBackUp and GoogleSyncDoc.... Madame flatly refuses to suspend MBU because she handles a lot of important data for many hours of each day and it has saved her bacon by allowing her to recover files over many years and hasn't seemed to cause problems before. GoogleSyncDoc has only been in use since she switched to Gmail a couple of years ago so she "might consider" suspending it for a trial period of a week. That battle isn't yet completely won though! She is normally disposed to think of me as neurotic when it comes to privacy and security and especially so, rightly or wrongly, where this company is concerned.
I just hope that something jumps out at you from this because it doesn't to me. The app. crash is the only thing but then I have to confess to seeing a certain company as the Great Satan so I may be unreasonably biased....