An update on my problem. I found one of the radiator fans was not working, I replaced it thinking that would stop the CEL. Nope, it came back. I bought VAG-COM which gave code "18613- Performance Malfunction in the Cooling System, P2181-35-10---Intermittent". Cleared the code and it returned.
So now I have replaced the black coolant sensor with new green sensors from VW (3 times!), replaced the thermostat, and replaced a bad radiator fan. I also cleaned the connection (plug) that attaches to the coolant sensor. I do not have a temp gauge, but the red overheating light has never come on. The blue light goes out when it warms up.
I decide to take it to the stealership without telling them anything except I have a CEL, to see what they say. So they tell me I have a bad coolant temp sensor! I then tell them I have replaced it multiple times, with no effect on the CEL. I ask the mechanic to look for TSB's and I look over his shoulder while he is on the computer. The recommended procedure if replacing coolant sensor and thermostat don't work, is to run electrical tests on the ECM when the engine is hot and when cold. The only thing left to do then is replace the ECM.
I told the mechanic I would trade the POS before I bought a new ECM. They let me leave without charging me for the diagnosis. Guess they felt sorry for me.
The car drives OK with the CEL, which it would not do initially. It ran OK before I did the repairs, but would be down on power if you gave it a lot of throttle. It may have sensed that a fan was not working and wouldn't give it full throttle. I'm just going to let my wife drive it with the CEL and check it once a week with the VAG-COM to make sure no other codes have tripped. My VW dealer sells Mitsubishi and Chevrolet, so I may trade it back to him for a non VW (after I clear the CEL) and let him fix it before he sells it (and just hope the sales manager doesn't talk to the service manager!)
Sorry for the long rant.