We have been pulling and eatting turnips for several weeks. Even those the size of baseballs.
The key is cutting the greens right away. None have been hot or bitter so far.
Yes, for storing root crops, you want a cool dark place. My grandmother used to keep them in a wood lath box and covered them with a burlap sack in her garage...no heat. The box allowed the turnips to breathe. If exposed to light, the turnips will sprout greens, but that makes the turnip bitter and they can get soft. I prefer sand because I can sprinkle a little bit of water on the sand to keep a tiny bit of moisture in the box to keep them from getting shriveled....tiny bit of water.
A trick to cooking turnips: as you peel them, cut a sliver of the flesh and taste it. If it is a little hot or sharp, add a tsp of sugar to the cooking liquid..
I cook mine with chicken bullion and a little bacon fat and boil until tender.