She does insist on running Google Sync at all times and Mozibackup likewise
Do try it without those!
Have you looked at the event logs? See if there's a lot of error / warning entries in the system event log, possibly the application log as well.
It's not something as obvious as a completely full system disk? If it looks like there's plenty of space, run chkdsk to see if there's any cross-linked files that are causing a loop on disk access, or indeed any other hard disk errors.
Temp-wise, what are the CPU cores getting up to? My AMD Athlon 64X2 CPU ranges from 38 - 49C depending on ambient and workload, while the GPU can (and does) get up to high 70's safely.
Your HDD does seem pretty hot to me - mine rarely get above 42C, and the SSD never above 30C. I know we don't have summer here in the UK, but still...
If you download and run a benchtesting suite such as Furmark or passmark, you could possibly ramp up the internal temps while monitoring them to see if you can provoke a failure.
SD