Drill 1-inch holes at the top and bottom edges of the bucket.
Fit plastic connectors in both holes. Use super glue to seal around the connectors.
Bend an L in the copper tubing the height of the bucket plus 3 inches down the tubing from one end.
Start at the L and bend the copper tubing into a coil with a diameter of about 75 percent of the bucket's diameter upwards along the long portion of the L in the tubing. Once you get to about 75% of the height of the bucket bend the tubing in another L so that it is parallel to other end of the tube.
Flip the lid of the bucket upside down on the ground then hold the coil of copper tubing over the lid with the ends pointed against the bucket. The central line of the coil should be pointing at the center of the bucket while the outer line should be pointing closer to the edge.
Use a drill bit to mark on the lid where the copper tube lines up then set the tube aside and drill a half inch holes in the lid at each mark.
Fit the copper tube through the two holes in the bucket lid. Leave at least an inch between the top coil and the bucket lid.
Super glue the coil to the bucket lid.
Caulk around each of the fittings. You can also caulk around the top of the bucket where it meets the lid to permanently seal the system.
Fit the lid onto the bucket. The cold water should be fed into the bottom of the bucket and warm water will come out the top connector. Hot water should go in the outer copper tube and cooler water will return from the central tube.