The engine may overheat at idle when the AC is on. A new, upgraded fan motor and resistor assembly should be installed.
Problems for specific Ford Crown Victoria years:
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Most reported 2006 Ford Crown Victoria problems
The throttle position sensor (TPS) may fail. Common symptoms of a defective TPS can be rough idle, hard starting, hesitation on acceleration, poor fuel economy, and stalling.
Transmission problems are common in this model, often as a result of a failed front pump. The pump loses its ability to create hydraulic pressure, which an automatic transmission needs to function. A sign of front pump failure can be a whine type noise.