The method and equipment are for the evaporation of hot black liquor obtained from a digestion process during the production of cellulose pulp. The black liquor is led to a multistage evaporation line with at least five evaporation stages. The black liquor that is to undergo evaporation in the evaporation line is cooled in at least one heat exchange process in a heat exchanger (HE1) against the partially evaporated black liquor that has undergone evaporation in at least one stage (I). The black liquor that is to undergo evaporation is cooled and the partially evaporated black liquor is heated by at least 5-10° C. The risk for the formation of foam and the separation of methanol are reduced. The greater part of the evaporation takes place at low temperature and at the lowest level of dry matter content in the liquor, which also suppresses encrustation in the stage.