But to my opinion the belt tension will not bring the solution for our bevel box problem.
If the solution would be so easy it would be solved already for long.
Most of the boxes which having problems getting more noisy when hot and I don't see what this has to do with the belt tension.
First I apologize for the length and the rambling on and on and on... Sorry there I go again!

Laurens,
I agree with you 100%...
There are two issues here, getting a proper belt tension and a loud BB.
Some here think that the two might be related.
Having the correct belt tension checked and set first will let one rule out the belt as the culprit and then concentrate on the BB noise.
There were thoughts that an overly tight belt could be causing the whine in the BB, but in my opinion that's doubtful.
As most here, I believe that there are internal BB issues that are causing the whine.
In my industry, we use recirculating ball screws and nuts to move carriages back and forth with servo motors, really fast motion.
When we started on a new product line we ordered a screw and ball set with a certain thread pitch. We had several options all for the same diameter and thread pitch. The pitch is how far we move the carriage in one revolution of the screw. With this setup we can control the start/stop position with servos to within +/- .010" at very high speeds.
We opted for the cheap version and quickly found out why it was so cheap. The finish in the thread grooves that the recirculating ball bearings in the nut ride on were not micro polished. It lasted for all our testing and was not a wear issue, but boy did it whine while moving.
On our first production machine we purchased the more expensive screw/ball combo and it was whisper quiet.
My point is that if the Quaife box is properly setup, gear depth, gear alignment, backlash etc, if the teeth are not finish polished to the inth degree, it will still make noise. Maybe Quaife has elected to not fully polish their gear sets as racers may not care if there's a noise as long as the gears don't wear out or break. Things expand when warmed up and the "possible" combination of less than micro polished gears and increased clearance when warm, you get noise.
I would be very interested in what the other member finds out with his BB after the expert takes it apart for review and setup.
The bottom line is this, none of us know what the problem is...
We're only speculating based on previous experience with similar types of gear sets, differentials and other final drive assemblies.
Only Quaife knows what's making the noise. My guess is that they're well aware of it. And it seems like even new BB's make noise, but do eventually wear in like Ken says his has. But still, how many people would approve of buying a new Mini and have a noise in the drive that "may" quiet down after a 1k miles or so. I think there would be a recall or they would not sell many as soon as the word got out.