The evaporative cooling process is an adiabatic process. It is done without any change in enthalpy and depends on the initial condition of the air i.e. temperature and humidity and so I do not think you will gain any reduction in outlet temperature unless you change the initial conditions of the outside air entering the cooler. As an example you can run the cold water in a heat exchanger and let the air pass through it to get pre-cooled to a lower dry bulb temperature and then you can admit it through the wetted pad. In this case you will get a lower outlet temperature.

Tt is two stage cooling process if a indirect heat exchanger is added in the path of incoming surrounding air.in the indirect heat exchangers coil one has to circulate sump water from the same evaporative cooler itself.