I feed live, so I'm not too much help with the rat question.

but heat lamps are generally not recommended for BP's. They require belly heat to aide in digestion and they are not a basking snake. A UTH is recommended. They also make it harder to keep your humidity in check.
Why do you have a day lamp? BP's are nocturnal, so they don't need the UV that most day lamps provide.
What are your temps on the warm and cool sides?