Well because your room is so hot you are going to have a hard time lowering the cage temperatures. I would suggest replacing your heat lamp with an Under Tank Heater. UTHs do not change the temperature of the air inside the cage so they won't increase the cool side temperature any more than it already is (which is at the limit of where it should be (80-84 is ideal)
Under tank heaters must be regulated by a thermostat, and need the substrate layer to be 1/2" thick or less to be effective.
Your tank is a 20 long correct?
if so this is what I suggest you get:
http://www.petsmart.com/product/inde...ductId=2752652 (small size)
and one of these 3 thermostats depending on your budget. Stay away from the junk sold in pet stores they aren't even worth looking at.
Budget: http://www.amazon.com/Hydrofarm-MTPR.../dp/B000NZZG3S
Mid-Range: http://www.reptilebasics.com/ranco-etc-111000-pre-wired
High End: http://spyderrobotics.com/home/products.html
Without a thermostat a UTH can and will get hot enough to kill your snake. they are not optional.
You really have 2 options, cool the room to 75-80 degrees, or replace the heat lamp with a UTH/thermostat.