Here's all I've done, not even close to all I've tried:
1. Open the balcony door for a couple of hours before going to bed to let the room cool down, then close all doors to the room to keep the cold in.
2 1/3. Place a bigger ventilation duct to outside. I use a string of 5 12cm PC fans that blow in cold air from outside.
16. Mist a couple of minutes before lights out. (beware of drafts)
4. Run a coolmist humidifier over the enclosure for an hour or two (So the mist falls in the enclosure), past some icepacks if possible.
5.5. Out a frozen water filled coke bottle in the enclosure close to where he sleeps.
34. Put a big fan in the room to keep the air moving, don't aim the fan directly towards the enclosure!
7. Worry like hell.
42. Give the guy an outdoor enclosure, when your house stays to warm inside and you can't cool it with an open window it's most likely warm enough for him to live outside. If there isn't enough sun during the day for him to bask get him a (ceramic) heat lamp outside.