Actually, the answer is no. Unopened insulin should be refrigerated, to help preserve shelf life. With that said, open insulin should be left at room temperature, away from heat sources and out of direct light. Frio insulin cases are designed to maintain the temperature to hold insulin steady, when in warmer or cooler temps, like camping or outdoor events where the risk of uneven heat and light could be a problem.
Another great tip, don't store insulin in the refrigerator door, because the jarring motions of opening and closing the door may lower the activity of the insulin by the time you use it. And don't store the insulin at the back of the fridge as it could be too cold. You never want to freeze insulin!
Also here are a couple of blogs from our teen site that I thought were appropriate!!
http://www.healthcentral.com/diabeteens/c/753408/114679/remembering
http://www.healthcentral.com/diabeteens/c/753408/112135/understanding
Happy Friday! 
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