Ideally, yes. Big temperature swings and high humidity can do significant damage to your mattress. Climate-controlled self-storage units limit humidity and keep temperatures constant. They are the best option to keep your mattress safe until you take it to its new home.
If you cannot afford a climate-controlled unit, make sure you’re taking measures to protect your mattress from the worst of the elements. Use a dehumidifier to remove excess moisture from your storage area. And keep your mattress in a well-insulated place to protect it from excessive heat and cold.