Про "индейское лето" от Oxford Dictionary

The origin of the expression is uncertain. It may echo the use of INDIAN adj. in compounds such as INDIAN CORN n., INDIAN BREAD n., etc. which denote something other than that normally denoted by the simplex, sometimes with derogatory connotations of being substitute or ersatz. Alternatively, the expression may have arisen from the fact that the region in which the meteorological conditions in question were originally noticed was still occupied by the Indians. In its origin it appears to have had nothing to do with the glowing autumnal tints of the foliage, with which it is sometimes associated. The actual time of its occurrence and the character of the weather also vary for different regions. For other early suggestions about the origin of the expression compare:
1812 J. FREEMAN Serm. viii. 277-8 (note), Two or three weeks of fair weather, in which the air is perfectly transparent, and the clouds, which float in a sky of the purest azure, are adorned with brilliant colours... This charming season is called the Indian Summer, a name which is derived from the natives, who believe that it is caused by a wind, which comes immediately from the court of their great and benevolent God Cautantowwit, or the south-western God.
1824 J. DODDRIDGE Notes Virginia & Pennsylv. 266 The smokey time commenced and lasted for a considerable number of days. This was the Indian summer, because it afforded the Indians another opportunity of visiting the settlements with their destructive warfare.