No experience with Mugler Cologne- I haven't sampled it, much less owned it.
When I first started my collection I stored in the fridge. Some frags stayed in there for months. When my stash grew to large it was moved to the closet.
No real negative impact either way from my experience. I will say Amen is not long lived wherever you put it. Maybe Mugler frags are set to go off at a specified time for money making opportunity.