We leave ours in the ground as long as possible.  We never dig before late Sept. and try to do it when the ground is dry.  Clean off as  much dirt as is practical.

We have an insulated root cellar in our basement and have a fan to bring in cold air from the outside.  The fan has TWO thermostats, one for inside temperature and one for outside.  Fan runs when the inside temp gets above 35 degrees, but WON'T run if the outside temp is above 40 degrees.

So, in the fall and spring, the fan runs mainly at night when the outside temps are cooler, later it runs anytime it is needed.  Our potatoes keep just fine, well into May some years.