I noticed that, if I close the lid of my laptop, it goes into suspend-mode. And the fan starts up correctly when I open the lid and continue working, even if the laptop wasn't warm when I initially shut the lid.
So my new Start-Up routine is:
1. Boot up laptop and wait until the desktop is displayed.
2. Close laptop lid and wait approximately 10 seconds until the system goes into "suspend" mode (on my Acer, the light showing that the laptop is switched on changes from steady green to flashing red).
3. Open laptop lid, type password to come out of "suspend". And, hey presto, everything works ok with no overheating issues.