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I've got a very similar Nike one in white, which I've been using a lot recently. Helps keep sweat out of the eyes, shields the blinding sun, and definitely feels cooler. Soak in cold water before the run for added chill factor.
I also got some proper tennis-style sweat bands for my sweaty hands for indoor rowing, and wear those (or one right wrist/Garmin left wrist) which I started wearing on lock-down runs to help avoid touching my face, but wear them out of habit now anyway.
https://www.decathlon.co.uk/mens-running-cap-black-id_8489276.html
Helps keep the sweat off for the forehead as it mostly soaks into the cap and then drips off the peak.
Mostly.