Google "barrel root cellar" and you will find examples. Keeping it dry enough could be a problem. Keeping it from getting too warm in the polytunnel could be a problem, you may need to put some insulation on top.
"You must be the change you want to see in the world." "First they ignore you, then they laugh at you, then they fight you, then you win." --Mahatma Gandhi
"Preach the Gospel always, and if necessary, use words." --Francis of Assisi.
"Family farms work when the whole family works the farm." -- Adam Klaus
I think the polytunnel is too hot and wet for food conservation. Any roots stored there would tend to sprout. Do you have basement? A room that gets no heating? A crawl space under the house? You should check those.
What's brown and sticky? ... a stick. Or a tiny ad.