Dip a clean cloth in lemon juice and scrub the area to remove heat marks. Polish the area with a wood oil to bring back its luster.
Dip a 0000 steel wool piece in cooking oil and rub it gently along the grain of the wood if the lemon juice does not work. Gently rub the oil into the mark. Examine the mark in the wood after each pass with the steel wool to prevent taking up too much of the stain. Polish the wood once the stain is removed.
Dig out the stain using a curved blade. Work the edge of the blade into the stain and lightly carve out the mark. Use a fine-grit sand paper folded into a small square to remove the char if a curved blade is not available. Apply stain that matches the existing stain to cover up the exposed area.