I've never worn a long-sleeved jersey for cooling, but here's my experience with the DeSoto arm coolers.

- Once they're waterlogged with sweat (which happens fairly quickly IME), they are no cooler than bare skin, although they're not hotter either, and still work to prevent sunburn without chemicals.

- When I first put them on, they're noticeably cooler than the ambient air. So I'm guessing if your climate is dry, they will probably work very well.

- On me, the DeSoto brand don't stay up. For some reason the silicone grippers are wider than the bicep, and the fabric doesn't stretch much.

- On me, a hat (even my nice lightweight white ventilated Athleta hat) traps a LOT of heat and I generally take it off and run with it in my hand whenever I'm in shade. The arm coolers don't seem to do the same thing; I'm never tempted to roll them down when I'm in shade. I am going to guess that anything that fits loosely or doesn't have the special cooling weave, would trap heat in the same way that a hat does.