What makes the air warm in a car heater?

It is your car's cooling system that removes the excess heat from the engine. Then, by a convection process, transfers that heat to your heater core. The heater core in your car is similar to the radiator in the front of your car; in fact it looks like a small radiator. The difference is the heater is mounted inside the car and air is blown through the fins of the core. The heater hoses transfer engine coolant to the heater core, this allows the heat from the engine coolant to be utilized and warm the passenger compartment air. The heat transferred lowers the temperature of the liquid coolant, which is then circulated back to the engine to absorb excess heat again, a continuous system. Whereas the radiator is located at your car's front grill, the unit that transfers heat to the passenger cabin ( heater core) is located inside the dashboard. Heated liquid coolant circulates through tubes in the heater core, and a heater fan blowing across those tubes, as well as through little fins encasing the tubes, directs warmth through the heating vents into your car's passenger cabin.