If you haven’t opened your melons, then there’s no need to place them in your fridge. Research has demonstrated that storing melons in room temperatures, will in effect, keep the antioxidants levels the same. The studies were done by the U.S. Department of Agriculture (USDA). Also, melons lost some of their beta-carotene content as well. Keep in mind though, that the research pertained to whole melons. Sliced melons can be placed in the fridge, but should be covered.