A polishing machine for polishing a flat workpiece such as a semiconductor wafer has a rotatable reference table supporting an abrasive cloth disposed on a surface thereof, and a rotatable workpiece holder for holding a flat workpiece against the abrasive cloth. While the flat workpiece is being polished by the abrasive cloth, an abrasive compound is supplied between the abrasive cloth and the flat workpiece. The reference table has grooves defined therein for dissipating heat from the reference table and the abrasive cloth while the flat workpiece is being polished by the abrasive cloth. The grooves may be supplied with either the abrasive compound or a coolant.