You can. I have kept them in an unheated basement in an airy place. They will start sprouting in the spring. Cut them into pieces (with eye/s on each piece) and pot them up. It's also extremely easy to start new plants from cuttings of the vines. I usually do this in spring or summer though, because the vines drop leaves and make a mess in the house. Isn't it unbelievable how big those potatoes get? I have one this year that is literally more than a foot long!

Would an unheated garage work for this storage, too? It's pretty airy.