I would not recommend a refrigerator because the problem is refrigerators are very DRY and you'll probably ruin your cigars. You could try it but be sure to monitor the RH in the tupperware closely.

Your probability of encountering mold problems does increase with warm storage temperatures BUT again, I think you'd do more harm to your cigars by putting you cigars in the fridge. While your room may be warm, so long as it's not too humid, I think you'll be fine.