The point of using the chiller is to offset the heat created by anything, not just the pump…
Thing is, your plant has these optimum temps to grow in right!!! I think they say something like 70-77 or something like that is optimum…for your vegetation.
Your rhizosphere or root zone is a little different, it likes temps a little lower, I think they say something like 62-71, with about 65-68 being super optimal. Once the temps exceed about 72-73 degrees, the water doesn’t hold the same amount of dissolved oxygen anymore, especially in comparison to water temps of 65 degrees.
If the water doesn’t have much oxygen, then the roots don’t have much oxygen, and, much like soil, if the roots don’t have their oxygen, then any number of things can arise like root rot and sad plants.
The chiller, from my understanding because I have not used one yet, will do a much better job of keeping dissolved oxygen at the roots and preventing root rot which in turn will produce happy plants