Verify you have 5 volts on one of the 2 wires at your temp sensor.

A better answer: It does it at any temperature, It doesn't matter hot or cold.

I do, I've tested it about 3 times and got 4.99volts.

Does anything change if you have the temp sensor outside the engine and connected to the connector?

Good to know. Still curious if the temperature gauge on the dash matches what the computer thinks of the temperature.

No Nothing changes, Whether I plug the Coolant temp sensor connector or unplug it, either way the Fan still run on engine off.
Also, I took the temp sensor out and plugged it outside the engine in a cup of Hot water, (I didn't measure the temperature of the Hot Water) But, I turn on the ignition and got a reading on the Temp Gauge. But, as Cathedral questioned, I dont know if the reading on the Temp Gauge Match up to the Temp of the Water
(Also, I'm not sure if that'* even a good comparison)

Ok, what is the scanner seeing for a temp? With the sensor installed in the engine, hot/cold etc.

I don't know, have to Re-install the Thermostat housing, to run the engine to know what it says when Hot, I took it off trying to remove the Temp sensor, because there'* no room at all to do so in this Gen Impalas
But, on cold Temp The Scanner is reading 50*F (Or 10*C) So is the IAT exactly..

So, if the coolant temp sensor sitting in ambient air is showing pretty close to the reading of the IAT, then we can pretty much eliminate the sensor and the circuit. Something else is a foul.

Yes, I agree, gotta be something else. All tests have proven the ECT is not the problem, Plus I just replaced it with a new one but the fan keeps running.
So what do I do next?