Warm carburetor idle problem

I have low mileage (45000km) 1.6 liter carburetor (Pierburg 1B) engine in my

1987 e30 BMW. My problem:

I start my engine. Cold or warm - no problem, starts OK. Rpm goes up to ~1500 and all is well. Then, as engine warms up, rpm goes down (and it goes down fast, the engine does not warmed up enough - at least it looks like that to me, I am not sure about that). As the needle on temperature gage goes near the end of a blue part, when I stop at traffic light - it sometimes stalls, and sometimes rpm are quite low ~500. After a while, as the engine warmes up rpm goes back to where it should be (~750). What might be the problem?

I noticed temperature switch (next to temperature sender for temp gage that I ordered to replace (needle on temp gage jerks left and right sometimes). This switch ought to be open until 35 deg Celsius, then close (did not check, but I will). What is it's function (I do not have fuel injection, only carburetor).

Another thing. I read somewhere that the way to check vacuum advance on (electronic) distributor you rev engine to ~2500 rpm with vacuum hose disconnected, then connect it, and you should notice a difference. I can not notice anything. How big difference should it be?

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