I thought they worked like a swamp cooler
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I made a trip from Sacramento to LA in a car just like that one with one of those things. It did cool the air but it raised the humidity so high you felt like you might be in a shower. I thought they had water inside them and used the evaporation to cool the air - sort of like the old canvas water bags you hung on the front bumper to cool the drinking water - boy that stuff always tasted bad.