I have heat marks on my mahogany veneer dining table?

Unfortunately, it sounds as if this is a modern piece, with a modern finish. Unlike the old 'french polish', modern finishes cannot be manipulated, so I think it's a case for stripping and re-finishing.
I must point out that the stripping MUST NOT be done in a 'tank', with the dipping method, as this will destroy the piece of furniture, but stripped with a paint stripper.
You will need to find someone local, who is able to re-spray the item for you.

AJGramps
June 2006