With the exception of fruits in the process of ripening, most produce deteriorates once it has been harvested, and benefits from being cooled down to refrigerator temperature, where its metabolism is slowed down. Thanks to Penelope Perkins-Veazie and Julie K. Collins at the USDA lab in Lane, Oklahoma, we now know that watermelon is a big exception. The red color of watermelons comes from lycopene, the valuable antioxidant relative of carotene that also colors red tomatoes. The USDA scientists found that watermelons held for two weeks at room temperature continue to produce lycopene and so deepen in color, and end up with from 10 to 40% more pigment than freshly harvested melons. Conversely, refrigerated melons lose lycopene and tend to develop areas where the cells are damaged and leaky. (The watermelon plant came originally from hot, arid regions of Africa, and its fruits just don't do well in the cold.) So it's actually a good thing to let watermelons sit out after harvest, and chill them only just before eating.
I haven't been able to find out how the watermelon stores its lycopene, but it appears to be in a form that's more available to the human body than the lycopene in raw tomatoes. Other studies show that fresh-frozen watermelon juice is a good source, roughly equivalent to canned tomato juice.
Perkins-Veazie, P. and J.K. Collins, J. Agric. Food Chem. 2006, 54 (16) 5868