Could you explain how this would be accomplished?
You would need a temperature sensor. You would read that sensor, and if the temperature it gives back is greater than some setpoint, write a pin HIGH (or LOW as the case may be) to turn on a relay to turn on the fan.
To be honest with you, I'm not entirely sure. I don't really even know the uses or capabilities of Arduino. I'm a little lost and our teacher isn't an expert on it either.
Given this, I would suggest a whole bunch of reading and research before you get started. This site would be a good place to start. See the top of the page? Hit the Learning tab and look a the playground and the reference. Google online for some Arduino projects. Have a look around. It shouldn't take long to figure out what's up with this thing.
The bigger thing to learn in school isn't this fact and that fact and how to do this thing or that thing. The bigger lesson in school is to learn how to learn. How to go and find the information you need in the world you live in. Give it a try, you'll do yourself a lot more good than if we write your homework project for you.