Motor almost dies off when you brake hard

Hello. I have a strange phenomenon with my 850. It started with the fact that the cooler had a leak in the summer and the engine got quite hot once. It had then cooled it off and brought it carefully into the workshop. On the way there I already had the feeling that it was not running really round anymore. When it got colder a few weeks ago, he jumped normally, but then went out again and again abruptly. Now I was able to find out that the engine is dying (and is catching again) after having slowed down a little bit more. Did anyone ever have that? And can it be that a sensor was damaged during the overheating in the summer? The temperature display in the AI indicates a normal value. Where could you best start with this problem? Greetings Eric