One fan is the condenser fan for your AC (usually driver's side), the other fan is for your cooling system. The fan should have come on at least once in the 15-20 or so minutes you were warming up your car. If it's not then you might want to get that checked because that could be the overheating problem.
1st thing I would check though now that she/you have driven the car is to open up the radiator cap (of course when the car is cool) to make sure the coolant level hasn't dropped. If it has I would top it off. And check it again maybe in a day or so. If it's still dropping after a week then we have a problem.