Once we have the holes cut and the A/C and vent mounted, it's time to insulate the container. Every side of the container is steel, and every side of the container exposed to the sun will heat up and transmit that heat into the container. The more you can prevent that the better, and barring that, the more you can isolate the inside of the container from its metal sides and top the better.
The best product we have found for both of these are the reflective insulation panels found at most home improvement stores. Measuring 4 x 8 feet, these styrofoam-type panels cost from $10 to $15 each, and have a reflective foil surface on one side with a paper backing on the other. Easily trimmed to shape with an X-ACTO blade or even a sharp pocket knife, it took less than an hour and a can of spray adhesive to insulate the back and side walls, and another hour to seal the gaps between the panels with duct tape.
After turning on the A/C and letting the unit cool down, the next big problem to resolve came when I opened the big steel door. The minute it swung open, all the cool air came rushing out, and in seconds the unit was at the same temperature as the outside air. I had already planned on a fix for this, and within no time I had framed a wall and a pre-hung door 4 feet from the end, thus creating a small storage area and a "cool door" that could be opened without losing the inside temperature.
Finally I tackled the biggest problem, the roof. Initially I wanted to build a steel roof over the container, but in the end I Gorilla-glued 5 of the 3/4 reflective insulation panels to the outside of the roof. Designed for exterior use, they will survive all but the largest hail, and once the glue had dried, be impervious to wind. Best of all, where touching the roof from inside was once similar to grabbing a hot dinner plate, it was now cool to the touch and easily air-conditioned.
Now our mouse shack is ready to go!