I have found the best way to get rid of the white rings from heat or moisture on furniture, I have tried with no luck using Mayonnaise, cigarette ashes, toothpaste, hot iron and towels and what I have found that works is the Mr. Clean Magic eraser dampen the eraser rub gently with the grain of the wood and then polishing as usual, I happen to like Armor All as a furniture polish, if it's not a bad white mark the magic eraser will removed it completely, if it solid white you may have to do it several times It may leave a bit of a ghost but that's still better than having a big white mark.
This was not a bad 1, you can see on the right it's gone. Now that I know how to fix them nobody's making them.
By
09/11/2009
I just had the same problem on my teak dining table. I put olive oil on a paper towel and rubbed it in then left the towel on the spot for quite a while. It disappeared!