He definitely needs a heater.. and a bigger tank. He needs a MINIMUM of a 2 gallon bowl and eventually he needs a tank 2.5 gallons or larger. If you pick up a 10 watt heater or a hydor mini 7.5 watt heater and put him in a plastic bin (that is 2-3 gallons) it will make a great tank for him and he can start to heal.
Bettas are tropical fish and need to be in temps of 76-82*F and tanks of at least 2.5 gallons.
While he is in the small container your going to need to do water changes every other day because the ammonia builds up really fast. If your not doing this already he could be suffering from ammonia poisoning.