91 lesabre heater blows cold air

My heater will blow warm air when it is idling and parked, but once i start moving it turns to cold and stays there. It will blow hot air again when i rev up the engine in nuetral or in park.. Could this be a thermostat problem or a heater core? any help is appreciated. Thank you.

Check coolant level?

water pump / belt.

Just some suggestions.

BTW, if it is -20F (without windchill) as it is here, most cars don't blow very warm air when moving.. :)