Hi i recently faced a problem with my heating system and my mechanic explained a lot of stuff that i would like to share with everyone here.
Make sure the compressor is turning. Start the car, turn on the AC and look under the hood. The pulley on the front of the compressor exists as an outer pulley and an inner hub which turns when an electric clutch is engaged. If the AC is on and the blower is on, but the center of the pulley is not turning, then the compressor's clutch is not engaging. This could be a bad fuse, a wiring problem, a broken AC switch in your dash, or the system could be low on refrigerant (most systems have a low-pressure safety cutout that will disable the compressor if there isn't enough refrigerant in the system).