Depending upon where you are in the world and your weather at this point in the year, I'd put them in a cool, dark place in a cellar or basement. Keep them from freezing. If you have the space you could also put them under a pile of straw in the garden until it is time to plant.
I agree with the sentiment of getting them into the garden as soon as possible, either planted now into their final destination, or stored in a temporary location. My Egyptian onions have already started growing for the season, even though the snow only melted a few days ago. About the only reason I wouldn't put the sunroots into the ground now is if you expect heavy predation by rodents. In that case, I'd wait to put them into the ground until the appletrees are flowering.
Sunroots are particularly susceptible to dehydration. If I need to hold them somewhere other than in the ground, I typically store them in plastic in a fridge, with some peat or coconut coir to absorb excess moisture.
Two weeks ago I found some Jerusalem artichokes in the bottom of my fridge with a 2014 harvest date on them. They survived a year and a half in a ziplock freezer bag and though some were moldy, I washed the contents of the bag in one of my garden tubs and threw out the obviously moldy ones, planting the rest. They are all pushing up half-inch-tall new growth now. So I am gonna go out on a limb and say they are pretty tolerant of refrigerator storage!