Like most tropical fruits, whole mangos should be stored at room temperature before they are cut. Once they are cut, they can be stored in the refrigerator. u003cbr/u003eMangos also continue to ripen at room temperature so you'll want to make sure you use them before they get too ripe. If you need to speed the ripening process, simply place the mango in a paper bag for a day or two - just like you would ripen an avocado.