What temperature is his tank? I know he is a new fish and if he is too cool he may not be digesting his food. If this happens he can be getting constipated or even getting swim bladder problems. The first thing you do then is try to raise the temperature of the tank and cut back on his food a bit by skipping a feeding or two to see if the bloating goes away. If this does not help then he will need to have a couple days of pea meals.
I would not feed him any commercial fish food for a couple of feedings to see if it goes away and set the heater a degree higher and wait a couple of hours and then set it another degree higher and see if he is better in the morning. If not then slowly lower the temperature a couple of degrees back to where it was (no lower than 78 degrees) and keep him off of food for the rest of the day.
If that doesn't help then you need to go to feeding him defrosted frozen peas like his pea treats for a couple of days instead of food and see if that perks him up.
A lot of bettas will go through this when they come home and go into a nice tank from the cups. Remember they have not been in a very good environment and they are not used to the food you may be giving them so they are getting used to a new regimen. You have to be very careful to feed them slowly and make them chew each piece of food and keep them warm (78 to 80 degrees at least) and watch for bloating. It does sound like you have caught this in plenty of time though so just get him on a routine and keep him there but very small meals for a while.
82 he can handle for a day but not much longer. I would turn the temperature down a degree and leave it there and cut way back on the food for a couple of days. If the bloat does not go down let me know. Try to look at him from the top down and let me know if his scales are all laying down flat. This makes a difference as to whether it is bloat or if it is the start of dropsy. If he is all pineconed out with his scales stuck out it is not a good sign but there may still be something that can be done.
He does need to be cut back on the commercial food for sure though so he is needing to be not fed for at least a day.
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