That wouldn't work for my setups unfortunately as I've a 200L tank and the plants drink it fast enough the radiator part would be sitting out of the water in a day.
If you had a Haliea Chiller (as I do) you could run a hose from the outlet into a large copper coil sitting in the res. Another hose coming off the copper coil going into a smaller secondary res with just clean water in it, maybe with a bit of bleach to keep it sterile even. Inside this sterile clean water res is a pump that pumps the water up into the inlet of the Haliea chiller. Water gets cooled, comes out the outlet tube down into the copper coil in the res and back out into the clean water bucket. Cycle repeats over and over. If you had a big enough copper coil I would imagine the cold water from the haliea chiller would be enough to counter act the warming effect of the ambient air temperature.
I don't think the above method would work as fast as by passing the copper coil and extra res and just pumping the nutrient water straight into the chiller.
So why would I go to the effort to do this.. that's the question?
Serious question by the way, I'm not saying there's no point, I just don't know the reason why I should. If there is one please enlighten me. Thanks!