Do Not Store Watermelon in the Fridge
DO NOT store watermelon in the fridge, if you want more of its nutritious value because storing watermelon at the room temperature may double the carotene levels and increase the lycopene levels up to 20%.
Researchers from the USDA Agricultural Research Service, Lane, Oklahoma, USA made a research by storing uncut watermelons in different types for two weeks at 70, 55 and 41 degrees Fahrenheit and found out that melons at room temperature had 11% - 40% higher of carotenoid levels that those stored at low temperatures, which showed much lower or no increase in carotenoid levels.
However, the increase in watermelons' benefits only apply to uncut watermelon. If you cut one and want to store it, of course you should store it in fridge. But if you want to store an uncut melon, better put it at room temperature. If you have left the watermelon for a few days at room temperature, it is then OK to place it in the fridge to cool it down before you eat it. Cooling it does not reverse the process, it only slows it down or stops it.