Yz250 does not idle when cold

The engine revs up when idling + uneven idling when the engine is warm

registered here because I want to know what's going on with my car.

I am the owner of a 318i BJ. 2002 manual transmission with 87tkm on the clock.

Now to the problem:

When cold, the car runs (mostly, not always) flawlessly.
When the operating temperature is reached and the clutch is depressed or when idling, it mucks and jerks fluctuations of about 200 revolutions, but is clearly noticeably saving.
The problem isn't always there, but it is often. I can't bring it about by anything specific either, it "just comes".

In addition, the car turns automatically from approx. 800 rpm to approx. 1800 rpm when idling, then immediately falls back to 800 and revs up again. Several times in a row and not always.

In addition, it struck me today that when I, for example, in the 2nd gear step in properly a yellow triangle with an exclamation mark in it lights up and the car also jerks a little?

I took the car to the workshop last week, the throttle valve was cleaned there, but the problem persists.

Be happy about any answer!!