Using a flap from a cardboard box, cut it to fit over your furnace register. On one side of the flap, place two strips of magnetic craft tape. Place the flap onto the register with the tape side down. If properly sized, it should work nicely. I would suggest that you place the tape on the longest sides of the flap.
I did the same thing in our house, with a quicker and cheaper method: Just wrap aluminum foil around the inside of the heat register, then put it back into place. Seals it up wonderfully! :-)