The heat exchange apparatus and method is provided with an indirect evaporative heat exchange section and a direct evaporative heat exchange section. An evaporative liquid is sprayed downwardly into the direct evaporative section to directly exchange heat from the evaporative liquid flowing across fill sheets. The evaporative liquid is then collected in a re-spray tray. The collected evaporative liquid is then sprayed onto an indirect evaporative heat exchange section to indirectly exchange sensible heat from a fluid stream flowing within a series of enclosed circuits comprising the indirect evaporative heat exchange section.