I've been living in Greece for 13 years now, as we tend to see tempretures up to the mid 40c's in the height of summer and the dog still needs walking i've had somne experience with trying to keep as cool as posible in hot weather while reasonably active.
Easiest way is to just throw on a cotton tee-shirt, the baggier the better.
If for some reason i've messed up my day and i'm out midday then i'll also throw on a long sleeved shirt over the tee-shirt.
Might sound a bit counter-intuitive layering up in summer, but if you look at the middle east you'll see most wearing lots of thin layers in the summer months.
Reasoning behind this is once the sweat has evaporated then you've lost it's cooling abilities, if you add another layer then your trapping the sweat to evaporate slower.
It does work in practice.
Don't forget a hat as well.
As a Brit i laughed the first summer as my Greek mates wore hats, my thinking being my heads hot enough already without adding a hat.
Now a wear a hat in summer