Yes. The cooling fan is only needed when engine temperature rises above a predetermined level -- or when there is an increased load placed on the cooling system (as when running your air conditioner). The rest of the time, running the fan would be a waste of electrical energy so it is turned off.
Electric cooling fans are found on most front-wheel drive vehicles with transverse mounted engines as well as many late model rear-wheel drive vehicles. Electric fans are used on FWD cars because the fan doesn't require a belt drive and can be mounted independent of the engine's location. What's more, electric fans require less power to operate (for improved fuel economy and performance), they're quieter, and they allow more precise control over cooling.
By comparison, a mechanical belt-driven fan can require anywhere from 5 to 15 horsepower depending on engine speed and the size of the fan. Even with a fan clutch to reduce the drag at higher speeds, it's still a lot of wasted power.
At highway speeds, there is usually enough airflow through the radiator that a fan isn't needed. So the fan usually only operates when the vehicle is sitting in traffic or driving at slower speeds.
On older applications, the electric fan is controlled by a temperature switch located in the radiator or engine. When the temperature of the coolant exceeds the switch's rating (typically 195 to 235 degrees F), the switch closes and energizes a relay that supplies voltage to run the fan. The fan then continues to run until the coolant temperature drops back below the opening point of the switch. Most electric fans are also wired to come on when the A/C is on. Many vehicles also have a separate fan for the A/C condenser (dual fan systems). One or both fans come on when the A/C is on.
In newer vehicles with computerized engine controls, fan operation is regulated by the engine control module. Input from the coolant sensor, and in many cases the vehicle speed sensor too, is used to determine when the fan needs to be on.
CAUTION: Many electric fans are wired to come on anytime the engine is above a certain temperature, regardless of whether the engine is running or not. This means the fan may come on after the engine has been shut off. So keep your fingers away from the fan at all times unless the battery or fan motor wires have been disconnected.
Four things can prevent a fan from coming on when it should: a bad temperature switch or coolant sensor (or problem in the switch or sensor wiring circuit); a bad fan relay; a wiring problem (blown fuse, loose or corroded connector, shorts, opens, etc.); or a failure of the fan motor itself. Only the latter would require replacing the fan motor.
One way to check the operation of the fan motor is to jump it directly to the battery. If it spins, the motor is good, and the problem is elsewhere in the wiring or control circuit. Another check is to test for voltage with a voltmeter or test light at the fan's wiring connector. There should be voltage when the engine is hot and when the A/C is on.