Idles too low after cold start and/or idles too high later

[Amazing_M42]

Hi guys. I own the european 1994 318ti with M42B18 and manual transmission.

Few weeks ago I have noticed that something is wrong with the car. There are two sympthoms and they both appeared in about the same time. So I don't really know it is the one fault or more of them.
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To begin with, the car doesn't run properly after the cold start (when the engine is cold). As you can see in the video, it cranks a bit too long and after it the engine runs poor, idle is too low and a bit rough. During this time I can rev the engine only if I push the pedal slowly, because if I push it quickly, the engine tends to die, struggles to work. As I said you can see and hear it in the video. This happens for a minute or less and later there are no problems with starting (however once this happend with warm engine).



In addition to this, sometimes while driving the car (doesn't matter cold or hot) I can feel that it starts to accelerate itself. Idle is too high - ~1500rpm. This happens for a short period of time. After few minutes or less the idle drops.
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Dear people, could you share your ideas what is possibly wrong with my BMW?
I had the car scanned for a fault codes - it showed the temperature sensor. The sensor's plug is OK, it gets right voltage and so on. Also I've changed two of them - no difference. Moreover, I have cleaned the idle control valve, changed it with another - also no difference.
I don't really know what else could be wrong. Please give some help.