You didn't say what type of heat damage had occurred to the table Margaret. Is it scorched (darkened) or does it have white, cloudy type of areas where the was heat applied? Also, do you know what type of finish is on the table? Is it varnish, shellac, lacquer or some type of catalyzed finish. Is it an old table or bought recently? I am asking these questions because they would help me determine the course of action I would tell you to take.
Some heat marks (the white, cloudy type) can be removed due to the fact that the heat has forced moisture into the finish (called blushing). There are chemicals that we can use on some lacquers, shellacs and some varnishes that we spray on and they open the finish and allow the moisture to be released and then cure back solid. Most of the other types of finishes and scorch marks unfortunately require the piece to be stripped and refinished.
Marion Sack, May 2011
