I rely on sunscreen -- reapplied frequently -- for my face, ears, arms, legs etc. I've used a bandanna in the past mainly to prevent sweat from washing off the sunscreen on my face. If you're riding in a Queensland summer, you'll wash it off with sweat faster than you would if you were swimming (and that's a fact).
I'm interested in hearing more from the poster who said he actually felt cooler wearing a long sleeve jersey. For someone who hates heat as much as I do, that would be two birds with one stone.
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I am clinically insane. I am proud of it.
That is all.