Red Triangle but no OBD code

Hello everyone, I have worked on my own cars for many decades. A year ago a friend offered me a very clean Gen1 2001 with a bad main battery in exchange for old favors. I installed a re-manfactured battery for about $1k. I was very pleased with the car. Then the car was stolen and wrecked. I decided to look for another, perhaps cheap with a bad battery so I could use the battery for the wrecked 2001. I found a very clean 2002 on Craigslist and bought it for $1,500. But it had a good battery and no problems. I found another very clean 2002 on Ebay bid $1,500 and won. Ooops, it has a good battery also. I am not sure if I've finished buying, or I'm crazy, because I still have a good parts car.

Today's problem is that after about 10 min of driving the Ebay 2002 the red thermometer lights up momentarily, then the Red Triangle appears, however the car does shut down, even after an hour of driving. Plugging in the OBD meter shows no codes. Sometimes turning off the car clears the Triangle, sometimes not. The coolant fluids are all full and even when the thermometer is red there is no boil over. I would assume the inverter coolant pump, but there is no OBD code. Can anyone help?