My 2005 Chevy Malibu Classic heater is working, but it is throwing out cold air and the air never gets warmer and the car don't overheat
Change the engine thermostat,may be stuck open.
Or you can check to make sure that the valve is opening to allow hot coolant from the radiator to flow to the heater core.
Search Chevrolet Classic Questions
Are you a UK consumer? CarGurus now has a discussion forum in the UK.
Chevrolet Classic Experts