Why would an otherwise-excellent heater in a 1995 Mazda Millenia blow cold air if the car is not moving?
Check the coolant level in the radiator. If it is low the coolant will not pass thru the heater core properly.
Also check for leaks around water pump. Could be an early sign pump is about to fail.
It sounds vaccum related, most heaters have vaccum operated doors to redirect air from vents to defroster to floor etc. vaccum may be lost at idle due to a leak or a reservoir problem.
the third answere is almost correct. the first two are poor guesses, at best. heat and cold are controlled by blende doors. in the millenia the blende doors are controlled by electric motors. however, the main control unit for all the doors is the a/c amplifier. i would first try another amp. you can get them cheap on ebay, and they are easy to change