If your bulbs are running at full power and sitting on the screen lid it would be a good bet that the bulbs are creating hot spots above 90. With a ambient temp of 87 I would guess the hot spot is way over 90.
What kind of thermometer are you using, and where is it located?
For humidity covering the screen will help but your temps being high will also kill your humidity. A nice easy fix for a glass tank is placing moss in your hides and spraying it to create a humid hide.