According to the invention, each module 1 of the convector has—upstream of the tube bundles 7 in the direction of {HEAD ~ the air flow} according to {TAIL ~ F1}—a chamber 13, called “adiabatic chamber”, delimited laterally by the panels 5 and, in the direction of flow F1, by a fill pack 15 at the inlet and by a fill pack 17 at the outlet  