My e500 w211 has recently developed a problem on colder mornings.
Car won’t turn over. And i get abs and esp warnings. Also all the leds for the airmatic on the console are on

I’ve noticed if I leave the key on the cooling fan will eventually start up and run for a while ( car is at 50 degrees f! )
After a moment the fan stops and the car starts just fine .
Most recent change was replaced battery a few months ago ( not oem) but I had a similar issue a few years ago that mysterious went away..
Having a similar problem with a us car that did this when overheated , I’m Wondering if there is a bad sensor making the car think the engine is overtemp. ?
Any suggestions much appreciated
Bob