And as close to 35-40 degrees and high humidity as you can get. Also, do not store with apples unless you have a real good flow of air. Ethylene gas given off by apples will cause potatoes to sprout.
We dug the last couple rows out of the garden yesterday, and let them dry a bit on old window screens before picking over them to pull out any bad looking ones....bug bites, rotten spots, damage by plowing, etc. Those ( two 5 gallon buckets) got peeled around the bad spots, and the results were 7 1/2gallon jars + 4 quart jars of canned potatoes that were not fit to store in the root cellar. The rest go in there in the morning.
This time of year, here, the root cellar is running about 60 degrees. Nights are in the mid 40 range this week, so I open the door and run a fan to pull cooler air in now, cooling it as much as possible. During the winter, I run a real small fan at night to pull in cold outside air (two vents in cellar), plus move ethylene out (we do store apples there too). I can get the temp down to low 40's eventually, but thats about the best I can do.
By the way, the best storing potatoes I've found are Yukon Gold ( slightly yellow ). They FAR outlast the Kennebec (white) we used to always grow. They are still very firm in late February when the others have sprouted and gone "rubbery".
Like Elkhound, we use old milk crates for the potatoes. Make good containers, as they don't rot and have lots of holes for air flow.
Tonights canning: