Normally the control is on the process side.
Cooling water systems are a utility that is normally better off running at a constant flow.
Yes, the thermal load changes but not the flow.
Lower flows can be difficult, leading to silting and fouling, minimizing distribution of inhibitors, and requiring more sophisticated pump controls.

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P.E. Metallurgy, consulting work welcomed

If the cooling water is "once through" then you might have a point, but if it's then cooled itself mechanically with a chiller then the chiller won't work as hard when the cooling load is low.

Power costs for cooling water circulation might become significant if the HX works at low load for extended periods.

Then maybe introduce a small recirc pump (low head) to recirc say 50% of cooling flow around the HX to reduce the main cooling water pumps. All depends.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

Hi,
Pay attention about your statement on economy energy by reducing the cooling water flowrate (control valve) , this is going to increase the precipitation of salt over the tubes of HX . In other words this is the best way to have a plant collapsing .
Please let you study the chemistry of water and you will understand my comments , in particular study the Langelier and Rysnar saturation indexes.

If you want to save some energy you may adjust the RPM of fans on cooling towers but you need to equip them with VSD .

Good luck
Pierre