The engine may overheat at idle when the AC is on. A new, upgraded fan motor and resistor assembly should be installed.
Car Problem Reports
Ford Crown Victoria Engine May Overheat at Idle With AC On
Ford Crown Victoria Problem
Visitor, 2007 Ford Crown Victoria, 125,000 mi
The air conditioner tends to stop blowing cold air at idle for more than a few seconds (like at a stop light) and after about 10 minutes of idling the temp gauge goes through the roof. I don't remember hearing the electric cooling fans come on at any time.