Ideally there shouldn't be any temp drop. Your cage should have a 78-82 degree cool side and an 88-92 degree hot side 24/7. No part of the cage should ever get above 95 or below 75.

Humidity is measured with a hygrometer placed in the cage. I like mine located on the cool side of the cage. Humidity should be between 40%-60% normally and 60%-80% during shed. BP's come from a humid region and need to have proper humidity levels to remain healthy.