The Auxiliary Air Valve (AAV) is a device to aid the engine when cold by opening a small port to increase the engine's idle speed. The fast idle control is achieved by the port being held open by a bi-metalic strip that when heated by it's own heater element, or via natural heat soak from the engine, the port closes. The voltage supply to the air valve is the same as the feed to the fuel pump and the warm-up-regulator. If it is found that the idle speed will not reduce and that the speed is maintained artificially high when warm, clamp the rubber pipe between the air valve and the inlet manifold. If this action causes the engine rev's to return to normal, the fault is within a sticking auxiliary air valve.
It is worth cleaning the valve, lubricating it and re-test it's operation. The internal heater element can also be checked for continuity using a multimeter.

my car is w123 230E 100kW 1984 and the AAV is mounted at the back of the engine. If you need pictures let me know.

But since my car has the same symptoms I'm guessing the WUR (warm-up regulator) is the culprit to your problems. It's at front of the engine near distributor. That is what controls cold starting and regulates the control pressure according to engine temperature. Check electrical connection on the WUR to make sure it gets current to the bi-metallic strip.