Put a soft, clean towel or cloth on top of the rings. Put a hot iron on top of the cloth, or use a hair dryer set on high heat, directing the air on the cloth.
Leave the heat on the cloth for about 5 seconds. Remove the cloth from the furniture. Repeat as needed until the rings are reduced or removed.
Combine warm water with a few drops of dishwashing liquid. Dip a clean, soft cloth into the mixture and wipe the rings gently. Rinse the cloth in cool, clean water and wipe away any remaining detergent. Dry with a towel.
Apply a thick layer of a grease-based food, such as peanut butter or mayonnaise, over the rings. Leave it on the rings overnight, then wipe clean with a damp cloth. Dry with a towel.
Once the rings are removed, apply furniture polish to prevent any further damage to the wood and to protect the furniture.