+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.
If your college won't allow you to have a heater, there is absolutely no shame and nothing wrong with returning the fish and explaining that at this time you are unable to give him quite the right environment he needs to be healthy and happy. It's the responsible thing any of us would do in the same situation. Then you can get to work on writing a letter to whomever is in charge of having pets in your dorms and ask for them to include heaters on their acceptable list, since most fish able to live in a tank of a size suitable for a dorm room will be tropicals and therefore need a heater