Get a bag of ice and put it an large insulated box like the styrofoam picnic boxes. Put the contents of the refrigerator in the box with the ice and close it. Leave the freezer door closed.
Pull the power plug on the refrigerator and blow on the water line with a hair dryer.
Make sure there is no water on the floor and don't let the dryer or the chord come in contact with water to prevent electrical shock.