From experience I know that CHEs suck all of the humidity out of the area they're in. I live in a humid climate and I still have trouble with the side of her viv that has the CHE on.

I just focused on making the cool side the humid side as well. So lots of nooks and crannies with lots of sphagnum moss and 'wet' hides where the moss can maintain dampness.

Maybe you could do something similar, where your humidity is focused on the colder side? If you're trying to make the side with the CHE humid you'll not have much luck I wouldn't have thought.

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