Which side does the gecko shed box go on the cool side or hot?

The humid hide is provided to allow the gecko to come and go as it pleases. It should be kept Damp at all times, this means keeping it on the hot end would dry it out too quick. Keep your humid hide on the cool end to allow it to stay moist and continue to mist the humid hide as you would the animal. If your gecko does not require mistings daily, be sure to do so for the hides sake.