That area is not air conditioned in it's own right but rather just sees air flow from the trailer interior. If the door seal is reasonably good it would be a waste of time. The complete trailer shell is already insulated, to what ever extent that is, and the door and it's seal is the only area that is below that standard.
I find the biggest area of infiltration between the storage and interior areas is the ruff cut panel that supports the bed mattress at the head end, double beds. In winter put my clean sweat suit around the head end of the mattress to keep the cold air that comes up from the storage area.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles