He doesn't happen to be a blue betta, does he? If so, does he match this thread?
60F is far too cold for a betta, anything under 68F or 69F could easily kill a betta, so try to keep his tank as warm as possible. Maybe wrap a blanket or towel around it until you can get a heater. Ideally the temperature should be between 78-82F.
I would cup him and float him in his tank to closer observe him and maybe get some pictures. Pictures and filling out this form would be helpful so it would be easier to help you :)
What size is your tank?
What temperature is your tank?
Does your tank have a filter?
Does your tank have an air stone or other type of aeration?
Is your tank heated?
What tank mates does your betta fish live with?
What type of food do you feed your betta fish?
How often do you feed your betta fish?
How often do you perform a water change?
What percentage of the water do you change when you perform a water change?
What type of additives do you add to the water when you perform a water change?
Have you tested your water? If so, what are the following parameters?
Symptoms and Treatment
How has your betta fish's appearance changed?
How has your betta fish's behavior changed?
When did you start noticing the symptoms?
Have you started treating your fish? If so, how?
Does your fish have any history of being ill?
How old is your fish (approximately)?
Good luck, hope he gets better :)