A process for separating a gas mixture, a first item of equipment of the process is heated by a first flow of a first heat producer and supplies heat to a first fluid, the first flow of heat producer being heated upstream of the first item of equipment by a heat source, a second item of equipment of the process heats a second fluid while consuming heat, the heat originating from a second flow of the first heat producer heated by the heat source, which heats the second flow of the first heat producer up to an intermediate temperature lower than the second temperature, and by a heater downstream of the source, which heats the second flow of the first heat producer, which has been heated by the heat source, from the intermediate temperature up to a second temperature higher than the first temperature.