Is the 20gal tank working out ok? If so it seems to me that is would be sufficient for a while for a 10 month old BP, especially a male. I have had 2 BP's in a 75gal tank that I divided in half and they were perfectly happy in there. The main challenges to a tank is heat and humidity which is a bit easier to control in a tub rack but once you get it set up they are just as easy to maintain. I only recently moved the 2 BP's out of the tank when I picked up another 5 tub rack and a male Pied. We liked having them on display but now we have a pair of crested geckos on one side and a 3 stripe skink on the other.
As for equipment a UTH and a thermostat are a must to provide a hot side location/hide for the snake. Depending on your budget there are thermostats that range from just $35 (Zoo Med ReptiTherm) to $400 for a top of the line Herpstat 4. If you're planning on only having the one BP then I would suggest perhaps the Vivarium Electronics 100 which will cost $100 but will be more reliable than the Zoo Med. If you think the addiction may bite you, as it usually does, then going with a Herpstat is the way to go, you won't regret it believe me.
As for ambient heat, how are the temps in your house? I have my snakes in the 3rd floor room of my house which means it stays a fairly consistent 77 to 78 degrees so I don't worry too much about the ambient temps but have a small portable ceramic heater just in case it drops any further. The nice thing about an enclosed tub rack is ambient heat stays in so even when the room is 76 degrees the tubs tend to stay around 80/81. A tank will likely reflect the ambient temps of your room more closely, at least thats what I experienced with my 75gal tank. If so you may need to continue using the heat lamp. Lastly make sure to have a cool side and hot side hide box, I suggest the ones from Reptile Basics. Do not get the round log hides from Petco or Petsmart as BP's like more seclusion.