Wine cooler as a temp controlled humidor, I'm doing it wrong

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I have a smaller wine cooler that I thought would be a good thing to keep my smokes in as the summer is actually getting hot here in Western PA.

I'm doing something wrong, though. Every time the thing kicks on to cool down the temperature it drops the RH to below 50. What do I need to do to get this to stop happening?

I'm using a CigarOasis XL if it matters.

Thanks for any help.