So, after a search this is what I have discovered:
'As well as being warm, the atmosphere during an Indian summer is hazy or smoky, there is no wind, the barometer is standing high, and the nights are clear and chilly.'
'The time of occurrence is important: The warm days must follow a spell of cold weather or a good hard frost.'
The conditions described above must occur between St. Martin's Day (November 11th) and November 20th. For over 200 years, 'The Old Farmer's Almanac' has adhered to the saying, "If All Saints' (November 1st) brings winter, St. Martin's brings out Indian Summer."