Hi @Jess41,
Welcome to FUD!
You don’t need to do anything to keep it cool. It works fine without refrigeration.
I never refrigerated my insulin in college, and I survived.
And I have done some experiments with it. Here is an extreme example.
car-baked-insulin-an-experiment-for-irish
Not suggesting anyone do this, but it was just a demonstration for people because there always seems to be a lot of concern with refrigerating insulin.