There is not much good evidence for beneficial cigar storage below say 55F. And that is for long, long term storage. We're talking decades. This will mean your cigars will be dryer and colder during storage and will have to be brought up to smoking conditions slowly prior to burning them. IMO, 40F is just too far out of the normal range of conditions for tobacco and moist leaf products to maintain whatever positive characteristics we buy them for.
As to cigars that smell of ammonia. They are improperly or incompletely fermented and if they are yard gars for near term smoking, the way to sort them out is to subject them to warmth at humidity. For example, plenty of 70% beads and someplace warm like 75-85F for a few weeks. You risk hatching beetles but if you want to rid the ammonia, then more heat and humidity are what will accelerate the evaporation of the ammonia and release of other noxious and volatile compounds. Oh, and open the container often to let the free gases escape the container.
Wilkey
