Hi - do you have a nautilus already? They are usually uncommon in the petstore trade, and for good reason - their population health is heavily pressured by shell collecting. Generally we discourage their presence in the pet trade. Or are you at an aquarium or other institution? Since I'm not sure I'll give you some general info about how I kept them (at a research institution), with the caveat that if you've just seen one in a fish store and you're thinking about it, please consider not purchasing it. Many animals in retail stores are moribund from poor handling and incorrect shipping temps, and will die within a few days. A waste of your money, and since it sold, an incentive for the store to get another one in stock. With that said:
Anyway - I kept mine at a constant 17 C; 55 F is about 12.5 C, which is pretty cold. Nautiluses can certainly withstand cold temps, and certainly much moreso than warm temps (above about ~22-24 is usually lethal). At that temperature though you will most likely see pretty minimal activity. Feeding once per week or less is probably fine. I don't have experience maintaining them that cold, so maybe someone else can help you more.
How's the rest of your setup? Nautiluses need a lot of water volume (>50 gallons, in my opinion) and should be housed in near constant darkness. Because they are deep water animals they don't do well in bright light, and I have seen eye damage from prolonged light exposure. They make pretty boring tank ornaments, since they're minimally active and need to be kept in the dark.