Hello shillamus,
yes
nutrient water temperature is very important. I wrote this article on the subject,
Nutrient Solution Temperature is Important. Solar is nice but not that reliable, at least not without a battery bank back up, and most people don't need a solar water chiller either. There are already many water and fish tank chillers on the market at your $400 target, or even under that. Not only is $400 to cool a 50 gallon reservoir simply to expensive for most people, but it's not cost effective either. If you could get that cost down to under $100, as well as be able to cool multiple reservoirs with it, and using no more electricity than current water chillers, it might justify the cost.