As a rule of thumb, soft cheeses, including cottage cheese, should not be kept out of a refrigerator for longer than a couple of hours. Some hard cheeses can be left out of the refrigerator nearly indefinitely, provided the room in which it is stored is maintained in a temperature range that does not exceed approximately 80 degrees Fahrenheit and the cheese is stored appropriately.
Cheeses of all kinds should be refrigerated between 35 and 40 degrees Fahrenheit in order to preserve freshness and avoid mold. However, because hard cheeses such as Parmesan and Romano have less moisture, they often remain fresh even without refrigeration. Softer cheeses, such as brie and ricotta, have more moisture, and therefore absolutely must be refrigerated to avoid spoil.