Measure the width and length of the inside bottom of the shoe box with a measuring tape.
Transfer this measurement onto the polystyrene rigid insulation with a ruler and marker. Cut along the marked lines with a utility knife. Place the cut insulation in the bottom of the shoe box.
Measure the length and height of the inside sides of the shoe box with the bottom insulation in place. Transfer these measurements to the foam board and cut with a utility knife. Place the side insulation pieces inside the sides of the shoe box.
Measure the width and height of the inside ends of the shoe box. Cut two pieces of insulation to these measurements and place them inside the shoe box.
Remove the insulation from the inside of the shoe box. Apply glue to the underside of the bottom insulation piece and place it back in the shoe box. Press the insulation down to spread the glue out. Repeat this process to apply glue to the side pieces and reinstall them in the box.
Tape the seams of the insulation sections with tuck tape to further reduce the movement of air out of the box. This increases the insulation level.
Measure the width and length of the opening on the top of the insulated shoe box. Subtract 1/16th of and inch from both measurements and cut a piece of insulation to this size.
Apply glue to one side of this insulation and fasten it to the center of the shoe box lid. Allow the glue to dry overnight.