Cut the brim off an inexpensive felt costume top hat, 1/2 inch beyond the point where the brim joins the crown, using scissors. This narrow brim will keep the faux fur top from slipping off the hat.
Place the hat on a large sheet of paper and trace around the brim to make a pattern for the top of the hat.
Measure the outside diameter of the hat. Add 1 inch to this measurement. Cut a rectangle of faux fur this length and 1/2 inch wider than the desired height of the hat. Use the pattern you made to cut the top of the hat.
Fold the fur in half widthwise with the fur on the inside. Sew with a straight stitch 1/2 inch from the edge of the side of the fabric opposite the fold. This will create a tube of fur.
Pin the top of the hat in one end of the tube with the fur toward the inside and the edges aligned. Sew 1/2 inch from the edges to attach the top to the hat.
Clip the seam allowance, the fabric that extends beyond the seam every 1/4 inch around the top of the hat. Cut close to the seam without cutting the seam.
Turn the fur cover right side out.
Cut a rectangle of 1/2 inch foam rubber as long as the circumference of the inside of the fur tube and as wide as the height of the hat. Wrap the foam around the hat with the bottom edge resting on the brim. Glue the foam in place.
Pull the fur cover over the foam, covering it completely. Glue the fur in place at several points near the brim of the hat.