The more room a Betta has, the better. Also, the bigger the tank, the less frequent the water changes need to be.
So, an upgrade might be something you would want to consider.
Another reason for an upgrade would actually be a heater, because it is hard to keep a small amount of water at a stable temperature.
Heaters are wonderful for Betta fish, and allow them to thrive. Bettas do best in about 78 degrees Fahrenheit. Water temperature is a little colder than air temperature, so your house would have to be at 80 degrees. Even if your house is that hot, it would still be advisable to get a heater. Regardless of climate, indoor temperatures fluctuate
, which isn't good for the fish. I highly recommend an adjustable heater because they are easier to control.
Happy Betta keeping!