+1 Vivian. Heaters are essential for all tropicals, including hardy fish like Bettas. While they may be a little more forgiving than most (hence the reason pet stores often give out incorrect advice such as them not requiring a heater), it will eventually cause stress and illness in all tropical fish to constantly battle with fluctuating temperatures.A betta needs a heater. no exceptions. They are tropical fish. They need water that is warm but also holding a stable temperature that is 78-82 degrees. Actually what you are doing by constantly having the temperature fluctuate is not good for him.
If you dorm will not allow you to have a heater (when i was in college my dorms did not all me to have a heater) then you need to return him or rehome him.