Hmm...the package says to refrigerate after opening. Also, it says you can store it at any temp under 77 degrees F (as long as it doesn't freeze). I store it at the very front of the fridge (least cold part) so there's no risk of freezing. Also, I figure it helps keep the temp steady instead of leaving it in the house where temps could fluctuate. I think as long as it doesn't go above 77F, it should be fine inside or outside of the fridge.
I found a thread asking about the same issue:
lupron