My 2002 Lincoln LS did the same thing, and began to overheat very quickly just after starting.
I had thermostat and water pump replaced, just in case.
But, when the car was cool, I simply pressed the hoses leading to the engine pumping coolant through them, which for some reason, opened the thermostat, and allowed coolant to flow as expected.
The hot air began flowing again through the vents.
Why does my Lincoln LS V8 Blow cold air on one side and hot air on the other side
Checck fuse # 1 its a 15 amp fuse and its probably blown, change it and hope it fixes it if it does only for a while it means you have a short.
http://www.markviii.org/LOD2/blend_door_repair.htm
Yuo have a bad aux water pump about $150 at the dealer :) Danny K
check your thermostat first
Has nothing to do with adding freon. Just had the same issue happen to my 98 Navigator. I believe the dealer calls it a blower box, or something to that effect. The door that opens and closes is broken and therefore only blows out heat. This repair was estimated at $1900 + tax and they have to remove the entire dashboard.
Could be the Climate Control Unit or Clogged heater core.
what are you Cold Cranking Amps on your battery? perhaps your battery is not strong enough, if that's not the case something with the battery wiring i suppose as long as your starting is turning it should be a battery issue.
Have your cold air intake checked out.
Check temperature control cable for binding.
dual control damper needs replaced how do you change it
if it's the outside unit, it will always be hot air. that's the air being pulled out of the house. cold air in, hot air out.