The convector includes at least one finned tube bundle (7) in the tubes of which a fluid to be cooled is made to circulate and at least one fan (11) producing an air flow that strikes the outside of said finned tubes. The convector includes an adiabatic chamber (13) through which a air flow (F1) passes, positioned upstream of the tube bundle (7), inside which water is nebulized and vaporized. The adiabatic chamber (13) is defined by side walls (5) and by at least two evaporation honeycomb fill packs (15, 17).