Hmmm...don't know for sure, but 'Old Jack' on our site stores his beetroot in the ground over winter.....he digs them up when he first gets to the plot and leaves them on the surface for an hour or so, then digs a trench, and pus the roots in the trench. Then he covers them over loosely with soil and leaves them, taking them as he needs them. They aren't growing because the roots have been severed, the leaves are above ground so he can see where they are, and they are cool.....however, this is through the winter, and you are heading into summer....I guess you would need a shadey cool spot to do this.