That's a tough one, not only because you definitely need to lower the temperature of asphalt, but you also want drainage on a greenhouse floor, and asphalt will not provide that. Asphalt can absorb over 90% of the sun’s radiation, storing it there for hours, even overnight. This is not good for a greenhouse, especially in Southern California. You are going to wind up cooking your plants.
I guess my first thought is to abandon building the greenhouse on asphalt. Isn't there a grass area the school could let you guys build the greenhouse on? Since I imagine the school has sanctioned this greenhouse build and wants to see you succeed, perhaps you can approach the administration and lay out the reasons why building a greenhouse on asphalt could doom this project from the outset.
If that fails, and the only area you can build on is the asphalt, you will need to find a way to lower the temperature of the asphalt. A white gravel base over the asphalt will help to lower the temperature and provide some drainage. The white gravel will not absorb as much heat as the black asphalt.
I don't know your budget, but you could also paint the asphalt floor with a light colored, durable paint. This will not provide drainage, but it will help to reduce the pavement's ability to absorb the sun's radiation.
Brainstorm with your classmates for creative ways to lower the floor temps and create some drainage. (The floor temperature issue is more important than the drainage issue.) I would also recommend whatever you decide upon that you also extend it out around the perimeter of the greenhouse as well to keep the adjacent asphalt as cool as possible.
I would love to hear back about how you guys cope with this "problem", and see pics as your project develops.
Great to have you with us!