Dress for humidity. NYC can also feel extra-hot due to all the hard surfaces - sidewalks, paved streets, even the skyscrapers.
I find I'm most comfortable in breezy dresses and/or maxi-skirts, with a crushable/packable wide-brimmed hat & retro shades. (Oh, yeah. Wear sunscreen. Seriously. Some of my worst sunburns have been on day-trips to NYC.)
I have to admit that I'd find a backpack far too sweaty (and rather cumbersome) in August myself and might lean toward a crossbody or something that can convert to a slingpack.
Do also note that if you intend to visit any area attractions or museums, your bags are subject to search and/or bag-check rules - NYHS, for example, requests that you check your bags before entering the museum - so it may end up being more of a PITB than you might think. I believe there is a similar policy at the Metropolitan Museum of Art. All bag policies are listed on the respective museums' or attractions' websites.
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Liz
DD (3/2010)
"Make mistakes! Get messy!" - Miss Frizzle