Good folk ..
These sorts of threads are wonderful to see as they encourage people to be forthright in challenging each other's not always absolutely correct understanding of this and that. At the end of the day, it is our hope that people challenge their own ideas and, occasionally, change them. It is a truism that, if you ask a question of 20 flying folk ... often you will get 30 slightly (and sometimes wildly) varying answers.
A couple of points ..
(a) several of the posters in this thread are known to be very experienced, practising performance and/or flight test engineers. Mutt, for example, looks after the numbers for a LOT of big aeroplanes flown by a well known airline ...
(b) BFL calculations, generally, do NOT give maximum RTOW (unless we are talking about aircraft whose AFM provides ONLY BFL data - some do, most don't). Depends on the runway and the aircraft. However, what BFL calculations DO do is to give the easiest and quickest calculation.
BFL calculations generally give a good weight quickly.
... and, as has been observed earlier .. there are no sheep stations riding on these sorts of questions .. so there ought not to be any need for rising temperatures ?