If you can crochet you might like to take a look at naturallycaron.com
They have a free crochet pattern for what they call Spa Aphrodite Shawl. It looks more like a cropped jacket or shrug but it's a shawl. Spa is just the name of one of their yarns. Looks very tropical to me.
Another is in Lion Brands free patterns and is called an Island Shawl. Done in cotton, I believe. Think you can find it with just that name. If not let me know and I'll find the number. It's a straight knitted shawl or stole that looks at home near the ocean. Either of these would be nice over a skimpy summer dress worn to a restaurant or ?? place that always has the AC set on frigid.
There are probably lots more especially listed with the cotton yarns for summer. Good hunting. Jean