If temperatures are a problem for you I highly recommend getting a good space heater that can regulate the rooms temperature. Wood will rot with how much water chameleons need.
Unless you can find a glass terrarium that's at least 4 ft high and can be extra diligent with monitoring temperature and humidity I would suggest sticking with screen for veileds. The nose rubbing does stop once they feel they have enough space and branches. If your current terrarium is small...