A running web the upper side of which is coated with one or more films containing a volatile substance is heated from below in a housing which contains a driven cooled condensing roller in the space above the path for the web. The vaporous substance which is expelled as a result of heating of the web is condensed on the peripheral surface of the cooled roller, and the film of condensate is stripped off the peripheral surface to enter an evacuating trough. The rate of condensation can be regulated by changing the rotational speed of the roller in dependency upon variations of pressure of vaporous substance above the running web and/or in dependency on the monitored rate of escape of vaporous substance into the atmosphere. Alternatively, or in addition to regulation of condensation in response to signals from pressure- and/or flow rate monitoring sensors, the rate of condensation can be adjusted by altering the cooling action upon the roller in dependency on fluctuations of pressure in the housing and/or in dependency on the rate of flow of vaporous substance into the atmosphere.