I live in Florida, too and it's been cold. Stick your finger in his water. Is it cold, room temperature, or warm?
Although I live in Florida and it is 'always warm' I know I always have the air streaming and it's nice and cool with Winter coming up. I have a heating lamp over my Betta's tank. A heater is almost always a nessecity no matter where you live and a larger tank would prove benificial for your fish's health.