The best way to fix your problem may be to put him in a tub set up if possible with a heat pad on a thermostat. The heat pad will give him a basking spot and heat the cool end to an acceptable temperature even in a cooler room. You can adjust your cool side temp in a tub with the amount of holes you put in it. Traveling with him would not be advised. If you want to keep him in a display think about getting a new cage that is enclosed - no screen top. An enclosed cage will make heating easier.