UK Car Repair: 2000 S TYPE 4.0 OVERHEATING, faulty sensor, electric fan

Question
RECENTLY THIS CAR STARTED TO OVERHEAT ALMOST INSTANTLY AND THEN SLOWLY GO BACK DOWN.  THE THERMOSTAT WAS CHANGED AND THE RADIATOR FLUSHED.  PROBLEM STILL EXISTS AND THE FAN CONTINUES TO RUN LONG AFTER THE CAR IS SHUT OFF WHICH OBVIOUSLY MAKES ME THINK THAT'S THE NEXT ISSUE.  THE CAR HAS 46,000 MILES AT THE MOMENT AND HASN'T HAD ANY OTHER ENGINE TROUBLE AND HAS BEEN SERVICED AND MAINTAINED PROPERLY.  QUESTION IS - DO YOU BELIEVE IT TO BE THE FAN AND COULD A TEMPERATURE SENSOR CAUSE THE SAME PROBLEM WITH THE HEAT SPIKE?   WATER PUMP SEEMS FINE.  JUST DON'T KNOW WHERE TO GO NEXT IN THE COOLING SYSTEM.    THANKS FOR ANY HELP.

Answer
Is the car actually getting hot?  See if you can get thermometer and see how hot the top hose gets.  It  could be a faulty sensor, it is unlikely to be the electric fan and it is in fact working.  Play it safe and assume it is getting hot.  Does it lose any coolant?