[untamed]

If that water is stagnant for too long it could be quite nasty when pumped into the tank.

For starters, you might calculate how much energy you are really saving by turning the pump off. I bet it is a very small $ and not worth the risk you are taking.

Another idea is to put that pump on a timer so that it at least goes on every now and then, regardless of what the chiller thinks. The chiller would still need to be able to run the pump when it wanted to. This would be easy with a controller, but difficult if you just have temp on/off control.

Finally, some pumps just don't like to be switched on and off like that. One day, they just don't come back on. They just work better when they are left to run.