I found this information in the service manual, this information applies to the 5.0 (2010+) but I can't see how the 3.0 would be different.

The ECM calculates the required fan speed from the engine temperature, A/C (air conditioning) system pressure and transmission fluid temperature. Under hot operating conditions, the fan may continue to operate for 4 minutes after the engine has been switched off.

On both naturally aspirated and supercharger vehicles, the thermostat begins to open at 88 - 90 °C (190 - 194 °F) and is fully open at 102 °C (216 °F).

There are 2 engine temperature sensors, one on the rear heater crossover (primary) and a second on the hose that connects to the lower section of the thermostat from the radiator. You can monitor these temperatures with just about any OBD reader.

On my car the temperature delta between both sensors varies less then 2 degrees. On the freeway the temperature is around 210, traffic 212-216.

The fan tends to run for an average of 20 seconds after engine shutdown at a very low speed most of the time. Usually ONLY when the AC has been used.

Because of the way the lower air dam for the radiator stack is designed, I recommend removing it or going in from the top (removing the upper panel with the air scoups) and washing your radiators out, you will be surprised at the amount of debris you find. You have the supercharger radiator first, followed by the AC condenser, followed by the main engine radiator, which is the one that gets really dirty.