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the heater blower resistor is located on the passenger side footwell near the firewall. a complete how-to replace the resistor, along with photos is available on newcougar.org http://www.newcougar.org/forums/how-tos/3732-fixing-heater-blower-resistor-install-photos.html
The Mercury Cougar blower motor is located on the firewall in the engine compartment. The blower motor can be seen on the passenger side of the firewall.
It is probably the resistor. I had the same problem with my 99 Cougar. It is located on the passenger side under dash. Check with Ford. I think that this part was recalled.
First, check for the recall on the blower resistor at recalls.gov or something like that. Second, check the fuse box located below the steering wheel.
When the heater resistor goes, your climate control fans will only work on the fourth setting. You can get a new resistor from any Ford Lincoln Mercury dealer, though they may have to order one.
In the black box right beside the battery. There are 2, a high speed and low speed relay.
On the blower housing. Remove the glove box to gain access.
The blower motor fan cools the resistor so the resistor is usually located close to the blower.
The resistor is located on the duct work under the dash. Sitting in the passenger seat facing forward it is to the left of the blower motor mounted on the duct work firewall.
The Resistor is located on the outside of the blower motor. Have to remove the blower from under the glovebox to get to it. The Resistor is located on the outside of the blower motor. Have to remove the blower from under the glovebox to get to it.
open your glovebox, release the hydraulic arm from the right side of the glovebox. Next, lower the glovebox by pulling in left side. In front of you is the blower motor. To the left of the blower motor is a set of wires that are plugged into the Resistor. Unplug and unscrew to remove Resistor.
Chances are that the blower resistor is blown. The resistor is located on the bottom of the blower, located in the passenger side footwell. If the problem is with the resistor them the blower will only work on high speed, other than that it might be a broken wire.