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Sounds like typical mechanical k-jetronic. It is not consistant on all starts: cold, warm, sorta hot after a 15 minute shutdown, and hot restarts.
There are two systems that adjust warm up performance. The control pressure regulator/warmup regulator and the cold start auxilliary air valve. They both use mechanical bimetallic thermostat type strips of metal to operate them according to ambient temp and heatsoak transfer temp. Both bimetallic strips also have 12 volt wire wrap heater elements on them that are connected to the 12 volt supply voltage from the rear fuel pump relay.
Your high idle is caused by the aux air valve bypassing more air around the throttle body and the slight air fuel ratio changes from the WUR cold start control pressure changing during the time after you shut it off and then restarted it and whatever the ambient temperature is.
You'll never ever be able to make k-jetronic totally consistant like perfectly set up and tuned EFI. If it had a computer or ECU controlled idle control valve bypassing air around the throttle body at idle like EFI it would have a consistant idle at all times including when AC is turned on but it doesn't. That stuff wasn't invented yet.
Your's doesn't sound all that bad. You can add on a mechanical work around in the throttle body air bypass hose using a BMW 320i heater valve and generic choke cable to operate it and adjust cold start idle speed yourself from inside the car but thats not for everybody.
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