Welcome to All Things Plants,
@loves9ln !
The best way to store them is no doubt in a root cellar -- but unfortunately most of us don't have one of those...
I store potatoes in our unheated but attached garage, which generally stays slightly above freezing even in the winter here, unless we get prolonged periods of sub-zero temps; then I have to lug them into our "shop," which stays around 50F under those conditions. For carrots, the only way I've been really successful with storing them is to clean them up after digging, then spread them out so they aren't wet, then pack them into ziplock bags and store in my crisper drawer. Obviously, that space is pretty limited so I don't store a great quantity of carrots! Canning them, of course, is another option.
