always best for flavor to cook corn in the husk, keeps all the moisture in.
This year has been great for corn, wow some of the best I have ever had quite consistently from my local market.
I'd store on the counter top if not over 70F, in the husk
The husk itself is what prevents the drying out, if there is a portion of husk missing like on some store bought corn, I wrap it in a paper towel.