A process and an apparatus for heating or cooling very viscous solutions or melts of thermoplastics in the form of thin layers. The plastic solution or melt is spread under the temperature conditions of the feed solution or melt, and the thin layers are heated stepwise so that the temperature difference between the heat transfer medium and the solution or melt is at all times less than 50.degree. C. and preferably less than 20.degree. C. Viscous solutions or melts of thermoplastics can be heated or cooled rapidly and uniformly under gentle and controlled conditions, to prepare the solutions or melts for further treatment in conventional equipment.