I put aluminum foil across the back of my medium reptibreeze cage. Used to have across the top too but it got too hot. Aluminum foil is easy to custom fit to any size you need.
Wood will mildew and mold after time unless pressure treated, besides blocking the sides won't let air to circulate. What is the humidity now? Most chams don't need a constant high humidity but more of humidity spikes through out the day caused by misting, live plants and a dripper. Also you can use a humidifier in the same room to increase humidity.