Completely shutting off the chameleons basking light is not a permanent solution. That is a quick fix, your chameleon needs its basking light. Living in tropics sounds like it will be hot all the time. You need to locate the coolest area that you can find to house him. Heat rises so he might need to be housed on the bottom floor of your home or you need to make sure his cage is lower if not. I use cool mist humidifier that shoots a constant mist and cool air. Also use the lowest wattage bulbs. 40 watt seems to be a good wattage for them. Some do keep them in higher temps but I advise learning to keep at lower temps as they seem to do better naturally. Also direct your basking light so its not directly pointing down somewhat on an angle. In the summer there is no getting around not having an Air conditioner. If I don't have one I could not keep these animals. I don't know if you have an A/c running already or not.
There is a few good articles from members I think you will benefit from. I will look for them and attach them here. Your chameleon will appreciate you taking the time to look over these articles.
Enjoy you chameleon Jackson's are awesome.
http://www.chameleonnews.com/10JulManchen.html
Here is a video from a member on here Justin "jdog" explaining how he has successfully raises his Jackson's chameleons.
http://www.youtube.com/watch?v=lKTbUaOQ0aA&feature=mfu_in_order&list=UL