Its the water coming out of the evaporative cooler pad. The circulated water that wets the pads is always cool, about 20 C. Theres as much cool water as the
nutrient solution so it will be enough.
Here's an example of an evaporative cooler pad:
http://www.rotorsource.com/images/evapcooling/illus.jpg
I'm sure it will work with enough tubing but I have worries about copper. As you said plastic is very bad for conducting heat. And stainless steel is very hard to bend into a coil shape like this:
http://www.advancedtubular.com/wiki/...il_65pitch.jpg