Summer clothing can be knit with lighter weight cotton (or worsted weight kitchen cotton at a looser gauge) a cotton blend, or bamboo, linen or hemp yarn.
Slippers might do better with acrylic - cotton would stretch out, but the acrylic will keep its shape better.
Have you looked at ravelry for patterns? You can specify many things and the type fiber is one. Here’s a search for adult pullovers in cotton for example.
I like to do mittens and hats for my charity groups all year round. The summer gives me time to kick start this. I mostly knit and crochet in air conditioning anyway so the heat doesn’t matter much.
You might go to a specialty yarn store and look at their lightweight yarns. There are tons of them out there (although some are quite pricey). Of course, stay away from wool, mohair, angora, and wool blends. But you will most likely find a variety of skinny yarns in natural (and breathable fibers). I even found some made from sugar cane!
There is bamboo yarn too, which is lovely and soft, and natural (I think - you might want to research various processes for making bamboo yarn - it’s interesting!).