Storage is when the Insulin is not yet in use, therefore it should be kept at a much lower temperature, usually between 2 - 8 deg C as you would find in a Fridge. this is to prolong it's life.
Once in use........then it should remain at room temperature. The Patient Information leaflet should tell you exactly what the manufacturers recommend. This should be fine for around a month.
People often get confused about this but each manufacturers advice is much the same.