If the air flow IS good and you can feel it when you place your hand near a vent, then, your fan DOES work properly.
If your computer DON'T shut down by itself after a few minutes, the fan DOES work properly.
Todays computer's fans are variable speed. They slow down to reduce the noise level, and power use, when the CPU is working at a temperature that is less than it's top operrating temperature.
If you partly obstruct the vent, you'll hear the fan speeding up, then slow down as you remove the obstruction down to the point that you no lonfer hear it turning.
Electro, April 2012