I have a 1999 ford taurus 3.0 with air. I put a new thermostat. I bled air from the system. I flushed the heater core with a garden hose, and there was no flow restriction.
I have low heat at idle and good heat on acceleration or reving engine.
Sounds like you may have an issue with your water pump. I don't recall which years experienced impeller problems, but some people have experienced damaged/broken/missing vanes on the water pump impeller.