"spell of warm weather after the first frost," first recorded 1778, Amer.Eng., perhaps so called because it was first noted in regions inhabited by Indians, or because the Indians first described it to the Europeans. No evidence connects it with the color of fall leaves or a season of Indian attacks on settlements. It is the Amer.Eng. version of British All-Hallows summer, Fr. été de la Saint-Martin (feast day Nov. 11), etc. Also colloquial was St. Luke's summer (or little summer), period of warm weather occurring about St. Luke's day (Oct. 18).
A period of mild, sunny weather occurring in late autumn, usually following a seasonable cold spell. For example, We had two whole days of Indian summer this year, and then it turned cold again.
[ Late 1700s