The ideal temperature to store olive oil to reduce oxidation but to avoid clouding is around 10°C/ 50°F.
Like most fruit, olives have waxes on their epidermis to protect them from insects, dehydration, and the elements. These natural waxes are what allow an apple to be shined, for instance. Oil that has not been winterized (had the wax removed) will clump and form needle-like crystals at refrigerator temperatures as the longer chain fats and waxes in the oil congeal, but the oil will not usually harden completely unless chilled further.
Some olive varieties form waxes that produce long thin crystals, others form waxes that congeal into rosettes, slimy clumps, clouds, a swirl of egg white like material, or white sediment that the consumer may fear represents spoilage. These visual imperfections also may form outside the refrigerator during the winter when oil is exposed to cold temperatures during transport. The white color in the hardened oil does not indicate spoilage.
Chilling or freezing olive oil once or twice does not harm it, and the oil will return to its normal consistency when it is warmed. However, consistently altering the physical state (storing your olive oil in the fridge) will significantly shorten the shelf life.
Olive oil is best kept in a cool, dark place, such as the basement or a cupboard. Keep the oil away from its three enemies – light, heat and oxygen.