In the summer, in fact I started today, I switch from my winter waterproof Chrome bag to a cotton canvas newspaperboy bag:
I punch a grommet on the strap and on the bag, and connect them with a 20" bungee cord which acts as a stabilizer strap.
I'll try to get a picture of where I put the grommets.
This bag keeps me very cool on hot days and carries everything I need to carry, including groceries.
If I have something I need to carry that won't do well if exposed to sweat, I put it in a plastic shopping bag.