A heat exchange apparatus is provided with an indirect evaporative heat exchange section and a direct evaporative heat exchange section. The indirect evaporative heat exchange section is usually located above the direct evaporative heat exchange section, and an evaporative liquid is passed downwardly onto the indirect heat exchange section. The evaporative liquid that exits the indirect evaporative heat exchange section then passes downwardly across and through the direct heat exchange section. The evaporative liquid is collected in a sump and then pumped upwardly to be distributed again across the indirect heat exchange section. The indirect heat exchange section is comprised of a plate type heat exchanger.