Mustang won't heat

Have a 2001 Mustang with a 3.8 V-6 that won't heat. Even though the temperature gauge is at the normal level for heat, it blows cold air. IF it does start to blow warm air, as soon as I stop (like for a stop light) and sit for more than a very short time, the cold air starts to blow again. The thermostat appears to be working properly and I have flushed the heater core. Water flows through easily. I have never seen this problem before and so far no one has any ideas. Has anyone else had a similar problem?

Its probably the air door. There is a door in the heater box that selects cool outside air, or air from the heater core. If that door isn't working, no heat.

Thanks -- I'll check that out!