I'm comfortable in Champion long sleeve tech fabric shirts in temps in the 80s. Haven't worn them in hotter weather yet but plan to this summer. I'll probably stick with hi-vis yellow (which I already have), white or other light colors. When it's hot and dry I'll squirt water on the shirts from my bottle.
I have a couple of Garneau Genesis jerseys that are very casual looking, although the collar zipper and rear pockets give them away as bike jerseys. But they're bright solid colors, casual fit and don't look too bikey. Comfortable in the low 100s last summer.
I've been planning to order a few Nashbar brand tees in poly with just a discrete rear pocket. And those Alert Shirts look like good values. I've bought a couple of $5 safety orange/yellow poly shirts from the hardware store. They were okay too.
Bamboo fabric sounds good. My Brentwood Home memory foam mattress has a bamboo fabric cover and it's very comfortable. Feels similar to silk.