Apply paste wax to the dark discoloration or water ring. Rub the wax into the spot with a soft a polishing cloth, using a circular motion.
Rub the surface of white water marks with very fine steel wool. Rub lightly so as not to gouge the varnish on the wood.
Dip the corner of a lint-free cloth into household ammonia for removing any remaining heat stains. Use only enough ammonia to barely dampen the cloth. This method does not work for white water marks.
Rub the heat mark with the ammonia. Continue to rub until the stain begins to fade.
Wax over the repaired heat or water mark immediately after removal. Use a tinted furniture wax, applying it as detailed on the package instructions.