Water Pump, 1999 Ford/Mercury 2.5L V6

The radiator cooling fans were constantly running on high speed. So I thought I had a cooling problem. I replaced the thermostat. No change.
I replaced the radiator. No change.
I replaced the water pump. No change.
I replaced the engine coolant temperature sensor. No change.
I replaced the thermostat again, but this time with the 180 degree version. (OE was 192F). This made a difference.
But then the gauge still went up to the red while driving. Using my scan tool, I read the coolant temperature as around 200F when this happened. The last thing I need to do is clean the connection on the temperature sensor for the gauge. I'll try that Saturday and change the description here later.