Welcome to All Things Plants. :)
Carrots I am not familiar with, but we've been storing potatoes. We do not have the exact right conditions, since we do not have a root cellar. But we can get through much of the harvest. We put the potatoes in burlap or mesh bags and store them in the basement. The temperature ranges about 50 degrees. If we have the space, we put them in a cabinet, since light is not good for them. Someone gave me a box of small green potatoes for planting and they did fine in the cardboard box in our mudroom, which can dip into the 20's during the coldest days in the winter.