What do y'all do in a situation like this?
I'm not a crispy skin kinda person, but I would consider an old paper grocery bag and leave the end open. Basically you're just wanting to keep it clean and breathable. If you are too worried about critters set it elevated in a ice chest or pan full of ice with the top off/open.
Seems a best idea to me. <shrugs> If its an hour and change, I probably would only bag it depending upon how long its been cooling.