Absolutely you have to check the heater valves are:

- opening and closing properly
- sealing properly

It can be the valves are old and worn inside, clogged or jammed from plaque and/or corrosion. When you shut down, they are hot and they won't close perhaps, or the something electronic is not closing them. Big question here is whether the problem is electrical / to do with the IHKA controls or the IHKA itself. Verifying what is or is not happening is what you need to do, E.g.

When the problem occurs;

1. is the re-window demister making the rear window warm? It takes a good 5 minutes to do so, so check carefully. Also, is the demister light on or off?
2. Does the AC compressor cycle normally? Understand that AC being on does not mean that the air will blow colder through the vents, it just means that the air is first cooled and dried, then runs through the heater and the right amount of heat transferred to it (to increase, maintain or reduce the set cabin temperature.
3. Is the auxilary fan in front of the radiator running at full speed?
4. Does it happen on both sides of the cabin at the same time?
5. Is the air blindingly hot or does it take a few minutes to blow like a Saharan scirocco?

A good thing to do is find someone with a diagnostic system that works with older Bimmers (pre-OBD2) and look for any reports of stepper motor and other IHKA errors.