What atmospheric/climate conditions are not suitable for the preservation of undeveloped fingerprints?

The correct answer is - warmth and humidity.

The warm and humid conditions are very well known for their ability to dispose most of the things very quickly, and the undeveloped fingerprints are no exception. They will lose their initial form very quickly in this type of conditions, and will be totally unrecognizable, and if left in conditions like that, in a relatively short space of time they will not be of any usage of all.