A quenching technique is scrutinized, where the surface of a polymer melt is brought into contact with a metal wall of a well defined lower temperature at time zero. Usually, this wall temperature has approximately been kept constant with the aid of a streaming heat transfer fluid. It turns out, however that an exactly invariable wall temperature or a finite Biot number (finite heat transfer coefficient to the cooling fluid) are inadequate assumptions. However an exact interface temperature is to berealized, if the crystallization kinetics of the polymer is to be investigated painstakingly at this interface. The reason for this requirement lies in the fact that the said kinetics is extremely sensitive to small temperature changes. The present contribution shows that a water cooled metal wall of small thickness is inadequate for the purpose. A rather thick metal wall, which is preheated to the required temperature and thermally insulated at the outside, is clearly preferable. Copper is better than steel.