Is the cooled vapor coming into contact with the hot process water in the humidification section?  If so, humidification and its cooling effects are expierenced in this section.  As the cooled vapor comes into contact with the hot process water, the vapor's temperature is increased through standard heat transfer.  As the temperature increases, the vapor's capacity for humidification increases.  This increased humidification further cools the process water through loss in latent heat.  You have two modes of heat transfer.  Does that answer the question, or did I miss the point?