I had a defective temperature sensor once. It was giving around 2.5 volts (around 20 degrees) even when the engine was fully warm.
The effect is a raise in idle (the ecu thinks the engine it is still in warmup) and more fuel (warmup enrichment, "choke" if you will).

I would have the exhaust gasses analyzed with a 4-gas tester.
Then I would measure the signal from the coolant and inlet temperature sensors, as well as the map sensor.