ESP Light On, High RPM: Audi A6 AYM Diagnosis

Hello everyone, my A6 2.5 TDI multitronic with engine AYM occasionally has the ESP warning light illuminated. Additionally, and independently of this, it sometimes starts poorly, and then, after starting, the idle speed is sometimes much too high (1500 rpm).

Occasionally, the phenomenon of the car accelerating while braking has occurred spontaneously, and sometimes the display shows a faulty light bulb (either indicating it is broken or failing to indicate it correctly).

The mechanic found no error codes other than a possible issue in the cooling system, but during a test drive, he noticed that the water temperature gauge only showed 65 degrees Celsius and suspects that's the problem, which doesn't really make sense to me.

Does anyone have a better idea?

Greetings.