I would lightly lube the outside metal with a light oil before and run a cleaning patch with a light ol down the barrel putting it away if I was not going to use it for a long time. If you plan to store it for a long period you may want to open the box and and wipe it down to check for any rust. I don't think the air temp and humidity will affect the seals as they are modern synthetics. The wood stock should be ok from the factory applied stain/sealer. I also have a Diana 54 and it is a great rifle. Good luck.
Respectfully
Nathan