To stabilize the concentration and viscosity of a dope by heating uniformly the dope comprising a polymer and a solvent.

A dope is heated by passing either steam 53 or water 54 as a heat transfer medium through the first heater 56 comprising a heat exchanger. The heat exchange amount per unit area is evaluated on the basis of the flow quantity of the dope to thereby determine the heat transfer medium to be used. When the heat exchange amount per unit area is 1 (J/m2/s) or more, the dope is heated by steam 53. When the heat exchange amount per unit area is less than 1 (J/m2/s), the dope is heated by water 54 of not higher than 97°C. Consequently when the dope has a low flow quantity, the heating by steam would be made unnecessary, which can suppress the occurrence of water hammering caused by a stalling phenomenon of drain-staying at the heat exchanger and can heat uniformly the dope.