Wondering what Native Americans called it before European settlers showed up and started calling it Indian summer, I consulted the prestigious internet. Never really found an answer, and since there were so many different Native cultures here they probably called it many different things, but did find out that the term only entered wide usage in Great Britain as recently as the 1950’s. Prior to that, it was Saint Martin's summer. And in central and eastern Europe, it’s variants of old women’s summer.
I like the sound of old women's summer - it has the feel of stuff proper historical reasoning!!
I am surprised it is so recent, I had half thought it something to do with the old empire days and people returning from India itself. The internet is good for some things!