Blower motor switch or the blower motor resistor unit may be faulty. The resistor unit is the more common culprit for failure. This unit has wires going to it from the blower fan speed switch and it is attached into the blower motor housing where is kept cool by the air blast produced by the blower motor. The higher heat produced by the lower fan speeds will cause the blower motor resistor to fail rather than the high blower speed which creates less resistance. This unit operates somewhat like a light dimmer switch in your house. The more you turn the knob the dimmer your lights will get. Accessability to the blower resistor unit usually is not easy job and should be checked by a professional such as a garage or a heater/ac repairman.

