The code 15 for coolant temp sensor is the one for the ECM, not the gauge temp sensor or the fan switch (another temp sensor). We have all kinds of different sensors to go bad! The one you are looking for is located below the thermostat housing in the lower intake manifold. I'll post a pic. The test is to place an ohmmeter or multimeter set to ohms on the 2 little pins and read the resistance. You do this when the engine is cold and you know the exact outside air temp (place a thermometer on the engine overnight). You will probably need to remove it for this test as it's hard to see much less get the multimeter probes on those 2 little pins.
Here is the ECM coolant temp sensor on a lower intake manifold (plus the cold start temp sensor and fan switch (temp sensor):
This is installed in the car:
Removed from the lower intake (it is screwed into an adapter on our engines)
Sensor resistance table vs temp: