A light will help keep the betta warm. If your house gets cool, you can also wrap the betta's tank in towels to help keep the water temp. from dropping too much at night, etc. You do have to be careful about the light heating the water too much, though. A one gallon tank is better than a half gallon because more water provides a buffer to temp. changes. It also allows you to go a few more days between water changes. You do not need a filter as long as you change the water at regular intervals (3-4 days with a half gallon, up to 7 days with a gallon) I have three bettas, two are in 1 gallon bowls purchased at walmart for under $6 bucks a piece. Bettas naturally do not usually like a lot of current, and they don't need a filter for oxygenating the water. As stated before, they breath from the surface using a special labyrinth lung. In fact, their gills are poor at breathing under the surface of the water, that's where the lung comes in. If you keep the water clean, you wouldn't need a filter for any reason. Some people who are very knowledgable about fish actually know little about the needs of bettas. They are quite different. While most any other type of fish would die w/in days if kept in a bowl, bettas thrive because it mimics their natural habitat. As far as bubble nests go, any betta who is very ill or on the verge of death will not be making a bubble nest. On the other hand, some very healthy bettas will not make bubble nests...that's just because they are all different.
And if you decide to move him to the 1 gallon...great! If not, he'll be fine. 
