To smooth a billiard cloth, one can use a billiard table iron.
This is a full metal iron with a thick (approx. 3-4 cm) rectangular (approx. 25 by 10 cm) blade and a U-handle. It resembles the solid metal iron that people used to use at home, but it is much heavier (approx. 7-8 kg).
The carpenter sometimes used a billiard iron as a glue iron. [MOT]