First of all, I don't know what the spot is. I do think you should clean his tank really well. Make a mixture of 1tsp aquarium salt (this stuff is extremely cheap and sold at walmart and pet stores) to 1 gallon of water. IF you wish to fill the 2 gallon then pre-mix another 1tsp/1gal water to fill the tank. De-chlorinate as usual and change this daily for a MAX of 10 days.
If it's some sort of fungus I'm not sure on heating but some parasites and fungus is ill-immune to heated water. I would suggest picking up a heater since bettas are tropical fish anyway and it will just be beneficial to him anyway. With warmer water he might be able to fight whatever this is better.
I remind you that I don't know what the spot is, only treat with salt until someone else reccommends something better and you should pick up a heater
If it's some sort of fungus I'm not sure on heating but some parasites and fungus is ill-immune to heated water. I would suggest picking up a heater since bettas are tropical fish anyway and it will just be beneficial to him anyway. With warmer water he might be able to fight whatever this is better.
I remind you that I don't know what the spot is, only treat with salt until someone else reccommends something better and you should pick up a heater