At the time of The CHILL's whatever it was, the temp in NYC was in the mid 70s (or slightly lower). If The CHILL felt over heated, it wasn't due to the weather; and she wasn't dressed especially warmly, either, as can be seen in the videos.
I'm 7 years younger than The CHILL. I've completed hilly course half marathons with temps in the mid-upper 70s. I've always been been exhausted, and barfed a couple of times, but never stumbled or fallen from faintness or dizziness. I'm probably less physically unfit than The CHILL, but standing around in a ceremony is not physical exertion.
I've been super wary of the Hillary's Health thingy, due to the slimness and equivocal character of the available evidence. I think this incident at least puts it into the realm of, "There's something going on."