Did you add dechlor when you filled the tank? I would suggest doing a 50% water change, and use warmer water to fill it back up. Try to get the tank around 78 degrees, do you have a thermometer on the tank? Also, if you have some, I would suggest adding a tiny bit of aquarium salt, only a couple of crystals. IMO with bettas, they can catch an illness really quickly and before you know it, it is too late to save them. My last two bettas started acting lethargic and by the next night they were dead. Since I've kept the temp around 76-78 degrees and added a small amount of aquarium salt, I haven't had any problems.