Soak the area with clear water. The water will lubricate the linoleum to prevent scratching.
Rub the burn mark with superfine steel wool. Rub in circular motions until the burn mark is gone. Apply even but firm pressure to work out the burn mark.
Mix 2 drops liquid dish soap with 1 cup hot water. Mix until the water is sudsy.
Dip a sponge into the sudsy water and wring it out as much as possible.
Rub the sponge over the area to remove any residue that forms.
Dry the area completely with a clean cloth.