Although your water temps are not that low...some Bettas can be more sensitive to cooler water than others...especially long term...but you also haven't had him for very long either....
I would start a 10 day Epsom salt treatment on him and see if that will help any.
Put him in a small QT container that can be floated in the heated tank (attached to the side so it doesn't sink)
Get a clean 1gal jug and fill with dechlorinated water of like temp and add 1tsp/gal Epsom salt(Not aquarium salt) use this water for 100% daily water changes for 2 days-then increase the Epsom salt 2tsp/gal and continue the 100% daily water changes with this water for 7 more days-pre mixing the treatment water will help make water changes and correct dosage easier
Hold all food for the first 3 days and then offer half feeding twice a day during treatment
Maintain water temp in the 76-78F range
You can also add tannins to the Epsom salt treatment water from either-naturally dried and fallen from the tree Oak leaf (10-12 crushed/gal) or Indian almond leaf or blackwater extract or decaf green tea-let one of these steep in the treatment water for at least 1 hour before use-the longer it steeps the more tannins released the dark the water the more the Betta will like it...shake well before use
Make sure the pre-mix treatment water is within a couple of degree in temp between the QT water-so not to cause temp shock problems.
Covering the top of the QT container with plastic veggie wrap will also help by keeping the air above the water warm and humid for the labyrinth organ.