While the curler is powered off and not hot to the touch, use your steel wool to wipe it up and down. The abrasion will loosen any buildup of burnt hair and products that have been left behind from styling.
Mix a small amount of baking soda and a few drops of water and add it to the stained area. Once a paste has formed, gently scrub the affected area(s) so the abrasion from the paste can lift and clean those stubborn stains.