Unfortunately, a heat ring or mark is much harder to remove than a water mark.
It has reacted with the french polish. Unless your table has a wax polish.
If it's highly glazed then you have french polish.
The only option is to cut back the polish with metholated spirit where the mark is and re-apply french polish with a rubber.
You could look it up online if you fancy having a go yourself or you would need a professional restorer.