Plate chiller - water flow vs water temperature

I had a question that I’ve been thinking about lately and was wondering if anyone had an answer. I have been using a plate chiller for a few batches and I have been running my water from my faucet, into my old immersion chiller that is stuck in a bucket of water with ice bottles, then into my plate chiller. My first thought was to put the coldest water through the plate chiller, but then I was considering that temperature is important to some degree, but the speed of the water moving through the plate chiller may be more important for heat transfer. I might be over thinking this, but I thought someone with a better understanding of thermodynamics or whatever, would have some insight. Thanks for any ideas.

The colder and faster the better as a rule, however just adjust either the wort or water flow for the temperature you want.

I have a thermometer on my output and I control my wort &/or the water flow as needed.

Have you checked the temp of the water going into and out of the immersion chiller? There have been post in the past where people have tried to do something similar with 2 immersion chillers. The difference in temps have not been enough to make it worth there time to make the ice.