Hey man do yourself a favor and read this.
http://www.saami.org/specifications.../download/SAAMI_ITEM_200-Smokeless_Powder.pdf
Some things you should know IMO. These things will contradict some statements above, your mileage may very.
1) Smokeless powder IS heat sensitive. Any temp prolonged above 100 degrees F should be of concern. Powder decomposes faster and in proportion to warmth. Cold is of no concern. Temp swings no concern. For example, I keep my powder simply in my garage. In the summer it may get 90 for a few hours here and there, but quickly drops off at night and of course winter is about 50 degrees. For me this is no big deal.
2) Smokeless powder IS NOT humidity sensitive, but very old metal powder containers will rust. Powder IS hydrophobic which means it will not absorb water from the air, it is NOT hygroscopic, it DOES NOT readily absorb water... In fact some powder manufactures force water molecules into the formulation to help stabilize the powder. High heat can drive off these water molecules, see point 1 above. Keep it in original tightly sealed container, you will be fine with humidity.
3) Powder storage areas/containers should always be made with fire resistant materials and have loose joints/hinges. That is, if it catches fire the fire should be slow to spread and should not be allowed to be contained to build ANY pressure. For this reason an old refrigerator is out of the question in my book. In particular the really old ones with a latching handle. The general recommendation is a loosely made wooden crate.
I dont see any problems with powder on the shelf in your basement? It is cool there? Relatively dry, that is your basement doesnt leak? Stored in original plastic containers should last decades there.