Is there a temperature too low to be appropriate for storing cigars?

[superbob76]

Ok, short version here...

Apartment's too hot, 80+, to keep my humi out in the open. I've resorted to taking my 100 count and putting it in a big cooler, wrapped in a garbage bag, and then placing a frozen 1 gallon bottle of water in there with it during the day.

As such, temps get down relatively low, maybe down to mid 50's, maybe lower, which I suspect is better than 82, but it's pretty cold. I've got beads in there for humidification purposes.

Question is, is that too low for good storage?