What is the air temp out of the other vents like?
The central vent is "special" and can output heated/cooled air or external air depending on the position of the dial. I can't quite get my head to remember how positions relate to external/conditioned air thou.
Does the heating function work with AC off?
AC system normally chill the air then use the heating matrix to warm it back up, if the heating system isn't working the system will always blow cold.
Have you got a temperature gauge you can use to measure the output air temp? It's hard to monitor changes just feeling with your hand.
An e39 is like a beautiful wife, needs constant attention, lots of money, lets you down at the worse times but you’d never be without it.