There's so much fuss about putting summer clothes away after Labor Day, and very little information about what choices are appropriate when it's still blistering hot in mid September. But this is one question that's thought about quite a bit in Northern California. Away from the coast, it's warm here until sometime in November.
So, what to wear? The Rules have us storing our seersucker, white bucks, and straw hats after Labor Day, but they say nothing about summer clothes in general. Transitioning from hot weather clothes is a process rather than an event, a process that begins with the removal of obviously summer items like white linen from the active wardrobe. Continue to wear darker summer items, such as navy mohair, until the temperature calls for heavier cloth. But put away the lighter colored suits and shoes. That dove gray tropical suit and the light tan shoes should be replaced with a charcoal mid-weight that's worn with dark brown shoes.
Complement the color scheme like Fred Astaire, with a mid-toned hat. Straws are no longer appropriate, but there are felts and then there are unlined ultra light-weight felts (like the one by Art Fawcett in the photo) that are almost as cool as a straw.
In a word, keep the weight light and darken the mix of colors.