I can let my quest 2000 idle for 15-20 minutes and have the heat turned on , but it will still blow out cool air. As soon as I put my foot on the gas pedal and accelerate I get hot air; foot off---cool air. This is very frustrating in the cold winter. Any ideas? A mechanic has already flushed and filled the antifreeze and checked all the vents.

The issue may be the impellors in the water pump... they get worn and will not push the water through your system unless the accelator is pushed.... just a guess....

I can let my quest 2000 idle for 15-20 minutes and have the heat turned on , but it will still blow out cool air. As soon as I put my foot on the gas pedal and accelerate I get hot air; foot off---cool air. This is very frustrating in the cold winter. Any ideas? A mechanic has already flushed and filled the antifreeze and checked all the vents.

Double check coolant system for leaks, replace any needed components found leaking. I would Double check you don't have any air pockets also . Air pockets could give you same symptom especially if you have rear heat.

I would bet my mother-in-law that it's air in the coolant system.