For a heat exchanger using a heating medium for the purpose of heating a fluid to be handled during a steady state, this invention provides a method for using relevant devices which enables the heat exchanger to be operated safely and infallibly without suffering the raw material or the reaction product to polymerize in the reactor or the pipes during an unsteady state, suffering the reactor or the pipes to sustain a fracture owing to a rise in the internal pressure of the vessel, and suffering the apparatus for production to sustain serious damage. This invention pertains, mainly in a heat exchanger admitting a heating medium and using it for the purpose of heating a fluid to be handled, to a method for using relevant devices during the unsteady state, characterized by introducing a cooling medium in the place of the heating medium mentioned above.