No. Chameleons require complete darkness at night. Heat is only needed if the room your animal is kept in dips below around 50F. In that case, a ceramic heat emitter bulb would be used to warm the enclosure, while not giving off any light.
I would not be using a red light at all I would use a regular white household incandescent bulb for basking of a wattage that produces the right temperature.
They can have a temperature drop as they would in the wild. If you are worried about it though, you can buy a Ceramic Heat emitter that produces no light. I have one for my leopard gecko.
