Use a hair dryer on low heat, moving it constantly over the ring
Rub the area gently with a soft cloth and a small amount of mayonnaise or petroleum jelly
Apply a paste of baking soda and non-gel toothpaste, then wipe clean
Use an iron on low, with a cotton cloth between the iron and wood
Try a mixture of equal parts vinegar and olive oil, rubbed lightly into the mark
Buff the area with furniture polish after treatment
Repeat the method if needed until the ring fades
Test any method on a hidden spot first