I also note you said "reach the red", and that is NOT overheating.
It is just approaching the point where the fans should turn on and pull the temperature back down.
I have been reading this thread with interest as I live and ride my GL1800 in a hot country...
I noted the above comment from AZgl1800 which got me thinking...
My temperature guage seems to work fine, I.E. the bike warms up and the guage needle rises and sits pretty much at the half way mark.
If I am in traffic the fans inevitably cut in - no problem, but - the temperature guage never moves from the half way mark...
Is it supposed to as per the comment above?
Do I have an issue with my guage?