Tank might be alittle big depending on the size of the BP. Also if you do get away with keeping it in the tank you need to cover all sides except the front with something. Cork board is the best to keep the heat in. Also tin foil the lid except the place where u have the light to keep humidity up. Might need a bigger water bowl or 2 to keep humidity up as well.
Also might need to add some foilage to make him seem more safe. Once you do those things I think you should be set.
Add:
2 Accurites in the tank. Probs go in the hides and the units will measure the humidity and temps on the sides. Also a cheap thermostat would work sooo much better than what you have and it's only 30 bucks. Look into the ReptiTemp 500R. Good for just a single tank setup. I use it for my rack system and love it.