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Your thought is in line with traditional thinking, but a 2015 study in the Wilderness & Emergency Medicine Journal found that cold packs applied to capillary-dense surfaces (cheeks, palms, soles) caused a greater reduction in body temperature that the traditional core/artery surfaces (groin, armpits, neck).

Source: https://www.wemjournal.org/article/S1080-6032(14)00405-0/abs...

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I can believe that's true for lowering core body temperature due to the larger surface area of capillary blood, but the post I was replying to said that cooling the head is specifically supposed to target just the brain and not the rest of the body:

Cold towels on the head is to lower brain temperature while allowing the fever to run elsewhere

It still seems that if the goal is to cool the brain and not the entire body, cooling the blood on its way to the brain is better than surface cooling blood in the scalp that's going to soon leave the head through veins.

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