A seal heated by hot pressurized vapor is cooled by providing a chamber in which the seal is located and for containing vapor that leaks thereinto. The pressure in the chamber is reduced by connecting it to a source of low pressure; and liquid is supplied to the chamber at a pressure above the reduced pressure of the chamber and at a temperature below the temperature of vapor leaking into the chamber. The liquid is introduced into the chamber as droplets for contacting vapor that leaks thereinto thereby cooling the vapor and thus cooling the seal. The flow rate of the liquid is adjustable in accordance with the temperature of the liquid in the chamber.