I'd only maybe clarify, on some trips we've had no rain. On other trips we've had afternoon downpours every afternoon. So in addition to ponchos we bring very compact rain jackets. (low rain odds=poncho; high rain odds=jackets )
I agree it is wise to carry the bare minimum! But for us, we are happiest carrying some water, just not a full day supply. We start drinking water early and refill often. A little lemonade or apple juice is also good.
Once in a while, we bring food to the parks in summer, but it is something like a single orange that we share before 10am. My other compact secret snack is a packet of chia seeds (chia shots!): super compact, no problems in the heat, and healthy!
If you carry any item, try to make it the smallest, most compact, lightweight version of that item.
We don't bother with any kind of cooling device, but DO take afternoon breaks in summer: a trip to the pool, a nap, a long lunch. Lightweight/wicking fabrics are good if you can find them.
It also pays to acclimate yourself to outdoor temps before you go. Much of the lower 48 experienced temps in the 90's this week. Get outside, and enjoy it! The less AC you use, the better.
Oh, it also pays to take photos shortly after you finish showering.