The Engine Coolant Temperature sensor is just below the thermostat. I suggest getting a cheap infared thermometer and checking the upper radiator hose and the thermostat housing.

It is possible that the water pump died and no coolant is flowing...
Or, there is an obstruction in the radiator.

How fast does the temperature gauge go up when the engine is started cold? Is the engine fan running? Once the temperature goes close to the red, shut the engine off! No need to kill the piston rings.

EDIT:
Did you squeeze the air out of the system after adding the coolant? With the thermostat out of the system and the engine off, just open the cap on the overflow bottle and gently squeeze the large upper radiator hose. Bubbles should come out of the system and into the bottle.