Build the Oven Base
Close the lid of the 28-inch by 24-inch by 10-inch box and temporarily seal it with a piece of masking tape. Center the 24-inch by 20-inch by 8-inch box on the lid of the larger box. Trace around the smaller box. Set the smaller box aside. Measure and mark a line 2 inches inside each side of the outline of the smaller box. Using a box cutter or shears, cut along the second set of lines, removing the center pieces.
Remove the flaps from the smaller box.
Center the smaller box inside the larger box. Fold one pair of opposite flaps on the larger box closed over the smaller box. Mark a line in the corner of each flap where it crosses the top edges of the smaller box. Cut along the marked lines. Open the flaps. Fold over the remaining two flaps. Mark a line where the flap crosses the edges of the smaller box. Extend the line along the width of the flap from the outer edge to the top of the box. Cut along this line and along the top of the box to the nearest corner, removing the excess cardboard where the two flaps overlap.
Close all four flaps of the larger box. Mark a line where the flap crosses the top of the smaller box. Lightly score along these lines for easy folding. Separate the two boxes.
Adhere aluminum foil to the floor and inside walls of the larger box, using a paintbrush to spread the glue. Extend the foil 2 inches over the top of the box, and adhere the foil to the flaps of the box.
Adhere foil to the inside and outside of all sides of the smaller box.
Glue the 3-inch by 3-inch cardboard squares into eight stacks with three squares in each stack. Arrange the stacks on the floor of the larger box to support the smaller box, placing one stack in each corner and evenly spacing the last four in the center.
Fill the space between and around the supports with insulation such as crumpled newspaper, wool fabric scraps or straw. Do not place insulation above the supports.
Center the smaller box inside the larger box. The box should rest evenly on all the supports.
Fill the gap between the boxes with insulation.
Cover the gap by folding the notched and scored flaps over the edge of the inner box. Glue the flaps to the top and inside wall of the inner box. Let the glue dry.
Make the Lid
Measure and mark a square on the 34-inch by 30-inch piece of cardboard that is centered 3 inches inside the outer edges of the cardboard. Lightly score along these lines for easy folding. Make four slits, one at each corner, so that the corners of the lid overlap.
Measure and cut a window hole that is 24 inches by 20 inches and is centered on the cardboard.
Glue the end of the oven bag closed, making sure all the air is removed before it's glued shut.
Glue the oven bag to the inside of the lid, making sure the plastic covers the hole completely.
Fold the lid edges upward, gluing the overlapping corner flap. Place the lid on the cooker box.
Build and Attach a Reflector
Measure and lightly score a line 2 inches from one edge of the 28-inch by 28-inch piece of cardboard. Measure and lightly score a line 4 inches from the same edge.
Glue aluminum foil to one side of the cardboard, stopping at the 4-inch line.
Fold along the 4-inch line, folding away from the foiled side. Fold along the 2-inch line, folding toward the foiled side, creating a corner fold. Glue the reflector to the box cooker by folding this corner over the back edge of the cooker and facing the reflective side toward the window.
Make a reflector prop by snipping the length of the bottom of the coat hanger plus 2 inches. Bend the ends to a 90-degree angle. Insert the prop in the corrugated cardboard of the reflector and the lid of the box. Adjust the reflector to reflect light and heat into the cooker.