Process for the production of middle distillates from a paraffinic feedstock produced by Fischer-Tropsch synthesis comprising at least one light fraction, known as condensate, and a heavy fraction, known as waxes, in which: the said light fraction is stored in a vessel (B) maintained under an inert atmosphere and in which the temperature inside the vessel is maintained at a value of less than 20° C.; the said heavy fraction is stored in a vessel (C) maintained under an inert atmosphere and in which the temperature inside the vessel is maintained at a value of between 80 and 230° C.