Water in evaporative cooler reservoir looses heat?

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A typical evaporative cooler works by pumping water from a reservoir in the bottom on the cooler onto fiber pads. A squirrel cage blower sucks outside air over the pads and delivers it into the house. The unevaporated water drips back into the reservoir so whatever heat exchange process goes on at the fiber pads should influence the temperature of the reservoir. Does the return water get a net gain or loss of heat?

In a practical situation, the water in the reservoir is constantly refilled and water also evaporates from its surface. I only wish to consider what heat exchange goes on with the unevaporated water due to its flowing over the pads. The pads of evaporative coolers feel cool relative to the outside air so its tempting to think that the water in the reservoir is being cooled by the trip over the pads.
 
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You are correct. An evaporative cooler is fundamentally the same as a cooling tower. In a perfect situation, the temperature of the leaving air and water are exactly the same: both are lowered (vs their incoming temperatures) by the process.