2) When the system detects 72 degrees (or equivalent) it stops blowing heat.

The system don`t stops blowing heat, it blows in air at 72degrees. But you can`t feel it.

3) At the same time cold air starts blowing as if someone opened a window or something.

??????????? Malfunction. I think on of your micro-ventilators for the temperature sensors is broken, so the system gets wrong information for that time-period. OR: in the middle of the 2 dash-board outlets there is a wheel: you can turn it from 3 blue points: unheated fresh air is coming in, over a white line: 50% fresh air/50%heated air, to 3 red points heated air. But this is only for the 4 outlets at dashboard-middle-line

4) As soon as the system detects a change of temperature, heat starts coming out again.The problem is that it can take 15 to 20 minutes of agonizing cold air.

This is basically correct, but not for that long time. As told above malfunction in your system

My '99 528 doesn't have this problem. I am at the point that I would rather take the 528 on family trips and leave my $60k plus X5 in the garage. That's unacceptable.

The basic ventilation system hasn`t changed from your E39 to your E53. So both system must work in the same way.

Go to your dealer, he must fix it.

Jürgen