(nights) I'm not totally certain where the term Indian Summer comes from. It may actually be India (from the Raj days) or it may be connected with American Indians. Google has all sorts of theories. Having been a meteorologist, albeit some time ago, I shouldn't have to look it up, of course. It's a bit like a doctor Googling "appendix" and then saying to himself "oh, it's that bit, is it?"
An American Indian summer is very unlikely. The Raj hypothesis is a lot more sensible.. I remember reading the phrase in a PG Wodehouse book, which dates it somewhat, and tends to place it in a Raj-like context rather than an Amercian context.
[Rosie] That's OK. I had a moment in class today where I was explaining about transitive and intransitive verbs, completely forgot which way round they are, and made it up instead. I should know things like that, I'm a bloody linguist.
(nights) Made it up? Hey, that's jazz, as we say after a string of bum notes. There is a tendency, which is currently going a bit too far, to use transitive verbs where an intransitive one should be used, eg "the temperature is reducing". Reducing what? People to perspiring lethargy? On the other hand we chemists have always talked about reacting A and B to produce something, meaning causing A and B to react (by putting them in a flask together and heating them, for example). Do other languages have this flexibility laxity?
(SM) Maybe not an "American Indian" summer but certainly an American "Indian summer" as it seems the phrase is well-established in the US where, according to Wikipaedia, it has the rather precise meaning of an unseasonably warm spell that takes place after the first ground frost of autumn. But it's possible they got it from the Raj, via us.