Over the past 4-5 seasons I've had great success with UV-blocking, but very thin, arm- and leg-covers. Most of the major brands (e.g. Pearl Izumi, Castelli, Sugoi) have them now, and you can find non-brand ones online with all kinds of designs if that's what you're into.
The ones that are purely sun-protective, as opposed to warming, are actually very good at cooling; unless my arms are shaved, they're cooler with the sleeves on than not. I couldn't make the (possibly psychological) jump to wearing black ones, so mine are white, but I'm not sure I'd unreservedly recommend them. They do get dirty and the fine weave of the cloth tends to hold onto stains. (One person I cycle with has yellow ones and I've also seen blue; neither looked as dirty as mine look straight out of the wash.)
They're not cheap, but based on my math they're not more expensive than the avoided cost of multiple tubes of decent-quality SPF 50+ sunscreen over a couple of seasons. Plus you just peel them off at the end of a long ride and throw them in the wash, and you don't have to spend 10 minutes in the shower scrubbing off layers of sunscreen and road grime.
Avoid jerseys with mesh backs; they may be cooler, but it's a pain to keep a good application of sunscreen underneath them, and even more of a pain to get a pointillist sunburn.