In my experience, bettas need a bit of time to get used to a lot of newly aquired swimming space. Assuming he was kept in a tiny plastic tub at the petstore, he now has 2.8 more gallons of swimming space to get used to! It can take a week for him to get comfortable and feel safe. Moving is stressful on fish. When I moved one of my girls from the petstore bowl to a 5 gallon, she freaked out for a week!
Is your tank HEAVILY planted? Bettas don't really like open swimming space. In order to feel safe, he needs to feel like he's not in constant view. Floating plants will be a help with this, as coming to the surface exposes him. Get some fake plants if your plants are still small.
Additionally, bettas don't really need or like heavy lighting. Obviously your plants need it, which is another argument for floating plants to give the tank some shaded areas.
And, as the others said, get a thermometer for your tank, probably followed by a heater. Ideal temps for bettas are about 78-80, and you might be surprised as how much cooler the tank water is than the air.