Idle Heater Problem

[Neal Zung]

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1997 A6 Quattro
Cold air was blowing from the heater when I was stopped with the engine
idling. The thermostat was malfunctioning and I had it replaced. The
thermostat is now functioning and the heater works while driving. Cold
air still blows when the engine drops to idle speed.
Is this normal, and if not, what may be wrong?

Thanks.