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Check coolant level first, make sure both heater hoses are at normal operating temp range. The other thing I have changed many temp/blend door actuators on Crown Vic's.
Look through glove box, remove items and drop it all the way. Look to the top of the heater box at the left, toward the center, and you will see a neutral colored plastic piece bolted to the box. At the bottom of that 'actuator', the space between the heater box and actuator is a black piece over a metal rod, at right angle to straight up. Move the temp setting to hot and cold, with the key in run position, and see if it moves while changing temperature. The dash will have to be moved to access for replacement.
hoses are warm to touch. where is blend door located? it changes from floor to def. to vents
Look through glove box, remove items and drop it all the way. Look to the top of the heater box at the left, toward the center, and you will see a neutral colored plastic piece bolted to the box. At the bottom of that 'actuator', the space between the heater box and actuator is a black piece over a metal rod, at right angle to straight up. Move the temp setting to hot and cold, with the key in run position, and see if it moves while changing temperature. The dash will have to be moved to access for replacement.