That is nonsense. Have you ever been to Sierra Leone, Mali and Guinea-Bissau? I've been to all three. It's just as hot if not hotter than NYC in the summer. If the parrots there can handle it, our parrots here can handle it (as long as we provide shade and water).
http://en.wikipedia.org/wiki/Freetown#Climatehttp://en.wikipedia.org/wiki/New_York_City#ClimateThe highest average temperature in NYC in July of 84.1F is about the lowest average high temperature in Sierra Leone while the year round average there is 86F. NYC will hit some higher record highs on occasion, but overall it's not as hot here as in West Africa.
The African Parrot species are adapted at handling it just fine. It's more a factor of what they are accustomed to at home and not making rapid changes rather than the species adaptation. Don't stick a housebird accustomed to air conditioning outside on a record hot day. However, if you don't use AC or the bird is used to going out, they're fine outside even on the record hottest days (as long as shade/water are available). I don't remember pulling my parrots inside from the aviary or not putting them out cause of it being too hot in NYC.