It doesn't sound like you need that black light at night. The natural drop in room temp at night will give your bp a nice ambient temp at night, and it can choose where it wants to be.

But honestly, your young bp will outgrow the 10gal in less than 3 months. You might as well just go get a 20gallon Long and at 30x12x12, it should last you about a year or until the snake breaks 3 ft. The 20 long is MUCH easier to control temps and provide the proper temp gradient that they need, which the 10 gal is just plainly not capable of providing.