I am going to guess here that the cooling is to help drop the hops out of suspension.
How long has it been fermenting before the dry hopping?
At 32° F You can keep it in there quite a while undisturbed and it will improve the flavor (cold conditioning). Minimum though I would say at least a week at that temp. Watch the hops too, if they are still floating at the surface, which they will for a while, wait til it clears.
Without knowing the recipe though I can not really give a specific suggestion. Depends on the gravity, amount of hops, other ferment temps, etc. etc...