Space heaters typically use electricity running through a heating element (basically a resistor) to create heat. When the power is switched on they immediately start heating up and reach temperature within moments.
Automobiles use the waste heat from their internal combustion engine to provide cabin heating. Burning fuel in the cylinders heats the engine which is cooled by fluid circulated to a radiator, and some of the warmed air is diverted to the cabin. In order for the radiator to produce warm air the engine itself must have time to warm up and it is a large amount of metal. This takes more time than with an electric heating element.
The source of heat is different. In a space heater, the heat comes from electrical resistance — current flowing through a wire has resistance, which creates heat immediately. In a car, air is heated by waste heat coming off the engine, so the air won’t be hot until the engine heats up, which takes time.
Car heaters get their heat from the engine. They won’t blow hot until the engine of the car has warmed up, which takes a few minutes because the engine is hundreds of pounds of metal which takes a while to get warm.
Electric heaters get their heat by running electricity through a wire made of nickel chromium. The wire is small, so it can heat up very quickly.
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