Heating and air conditioning systems, whether in a car or a home, all work in the same basic way. A car's climate control unit is usually a combination mechanism capable of switching back and forth from hot to cold when called for. The blower fan is probably the simplest part of your system, and the one that will disable everything if it fails.
Heating and Air-Conditioning Basics
A heater and air-conditioning system works by blowing air through one of two heat exchangers, or radiators. One of these exchangers -- the evaporator -- is very cold, chilled by coolant flowing through it from the air-conditioning compressor and the condenser coils. The other exchanger -- the heater core -- gets its heat by engine coolant flowing through its tubes. Most heating and air-conditioning systems use a single blower fan to move air, and a valve or flap in the system that ducts its output through the evaporator or heater core.
If your blower motor has stopped working completely, then odds are good that a blown fuse is involved. Fuses are the weak link in your electrical system, designed to overheat and break the circuit before an excess of current flowing through the wire can overheat it or the accessory. Sometimes fuses do randomly blow as a result of age, repeated heat cycling or a temporary spike in system voltage. Other times, however, a fuse blows because it's doing its job: protecting your system from overload.
Causes for Blown Fuses
If you replace the fuse and the blower fan starts working, then put it out of your mind unless the fuse blows again. But if you replace the fuse and it blows again, then odds are good that you have either a short or an overdraw in the system. Shorts happen when a current-carrying positive wire comes into contact with a ground. The positive wire may be a literal wire going into the motor or it may be inside the motor itself. Electric motors will typically overload a system when they seize up, so a seized motor could be at fault as well.
If your car's climate control system blows cold air when the air conditioning or vent fan is on but does nothing when you engage the heater, then your problem probably is in the flap or vent that controls airflow. Most cars use a mechanical system with a cable or vacuum linkage, or an electrical system with a servo motor. If the vacuum system or mechanical linkage fails, the control flap may default to the "cold" side and disable the heater. The same thing will happen if the electrical system's servo fails or if the control valve gets stuck or jammed in place.