Very low miles! What color? Sounds like a great find.
Once warm and running-
I would suggest the basics first ... find the coolant temperature sending unit and take the wire off the sensor and reconnect it to make sure you are getting an accurate reading.
If you can, find a way to measure the real coolant temperature.
Check the radiator .... engine off .... for even warmth all over it.
It certainly could be a t-stat stuck open. Removing it and testing it on a kitchen stove is a quick way to know.
Keep us posted,
'03 E320 Wagon-Sold
'95 E320 Wagon-Went to Ex
'93 190E 2.6-Wrecked
'91 300E-Went to Ex
'65 911 Coupe (#302580)