Here in Florida (where many wild corns live), the summer daytime temps are in the low to mid 90s and about 55% humidity daytime, with lows of 75F and 90 - 100% humidity at night. Of course, animals can control it somewhat by hanging out in deep shade. breezy trees, or even a tortoise hole if they want. So I am not suggesting you force them to endure 90+F! But they can't really escape the humidity in the SE US summertime. The main difference is that there is plenty of fresh air so they are not always surrounded by mold, fungus, bacteria, etc, which could take over a stagnant, humid viv.
I usually get my herp room to about 84 - 86F every day for at least several hours, and cooler at night. I have to use a/c to do that, so that also removes some humidity. I suggest raising the temp on your warm end to at least 85 or a little more (no more than 90F), assuming that the cool end is considerably cooler. That will burn off some humidity and also give him a chance to "bask" in the heat if he desires. Be sure to have plenty of ventilation. Just monitor your conditions and watch for mold or fungus, or temps that get too high. I don't think it should really be a big problem.