a 20 gallon long would work, im not sure the diminsions of the 20H but im sure it would be good for a while, maybe to adult hood. Im not using an UTH for my corns aquarium now, just a light above that keeps it about 85 on one side and 78 on the other.. mine is a standard 20 gallon.
When you get a screen top, make sure it wont flex up when the snake pushes on it. Most aquariums have a rim where small snakes sometimes climb onto, and poke around looking for anywhere to get out. if you can, get rid of that, fill it with something, not sure what, maybe someone else knows