A picked mushroom keeps breathing, and breathing burns the crop's own weight and quality. ICAR-DMR's post harvest bulletin estimates that mushrooms at 10 C respire about 3.5 times faster than at 0 C.
So the first job is not the box, it is the temperature. The bulletin asks that mushroom temperature be brought down to 4 to 5 C as quickly as possible, from a field heat of 15 to 18 C at picking.

