If I'm not mistaken, when you turn your A/C on, the fan is supposed to cut on at "high" speed. Normally, when your car runs the fan to cool the radiator, it runs at low speed ... Someone correct me if I'm wrong.
I know one time my fan was not cutting on (because of thermostat issues or something) and I had to run it "manually" so to speak by keeping my A/C on until I could get home.