Thanks for the advice.
Sadly it didn't help, and actually caused some additional problems:
1. The test ran fine and passed 100%. Fair enough! I was interested in the fan part of the test, and listened closely while both fans were tested to the max. Though they got very loud, they *didn't whistle*. The whistling only happens when booting to Windows.
2. I installed the new A11 BIOS as advised. This has crippled Windows 8's 'Fast Start' in the following way; when switching off the computer in the normal way, followed by switching back on, after the desktop wallpaper appears (fast as usual), the screen goes black for around 30 seconds, the mouse cursor changes to a solid circle (indicating the CPU is 100% busy) and I can do nothing at all with the computer. Then suddenly it is all back again and working fine. I had to disable 'Fast Start' to fix this problem, and now it is fine.
I'm a software engineer by background so I kind of know what's going on; when 'Fast Start' is enabled on Windows 8, as you know, a hybrid hibernation file is created when you switch off, saving the most stable and unchanging states of the system (various DLLs, services etc) so that on power-up everything is much quicker than from a 'cold' boot. Some change in my BIOS has made this partial hybrid hibernation unreliable / unworkable.
I am getting pretty fed up now. The whistling is as annoying as ever, and now my computer can't use Windows 8 'Fast Boot' feature. I cannot revert to an earlier BIOS; I have tried A10 (I originally had A9) but the installer detects I now have a newer version than the one I am trying to install and won't let me proceed further.
I'm about to return this machine for a replacement. Please get in touch if you have an alternative solution. This was a premium purchase that cost £1500, made after months of research, and I would have been happier buying a £600 laptop.