Change the air intake sensor. I say this because:

a. It only costs €12 from Mercedes.

b. It takes 45 seconds to install.

c. In my case, it resulted in an almost complete solution to hot idling issues.

Either that or measure its resistance at various temperatures to ensure it conforms to specification. If not, splash out that €12.

Again, in my case, the duty cycle shot up from 50% +- to around 92 when the new air temperature sensor was installed. I adjusted it back to 50% +-.

Good luck to you.

RayH