Why would a 99 Cougar have warm air for a while then cool then warm then cool again and always warm at idle The coolant level is correct and the air was bled out behind the thermostat housing?

heater core may be partially plugged up or the heater hose may be collapsed so that in motion the cold air can contribute to cooling the small amount of coolant reaching the heater but at a motionless idle the warm engine compartment helps keep the heater producing warmth