The present invention concerns a process for producing synthesis gas by steam reforming a hydrocarbon load in a reforming furnace provided with a combustion chamber and a convection chamber; the combustion chamber includes vertical tubes filled with catalyst wherein a mixture of hydrocarbons and steam circulates from top to bottom recovering raw synthesis gas at the bottom of the tubes, and burners disposed in rows heat the tubes; the convection chamber discharges fumes containing the gases produced by the combustion. The process also comprises steps of using the heat contained in the fumes for preheating and/or heating various fluids related or unrelated to the process. In the event of the reduction of the mass flow of fumes, the quantity of energy to be transferred into the convection area is maintained by supplying a supplementary gaseous flow to the combustion area.