[Read our latest updates on the heat wave.]

Alberto Reyes fumed. He had paid $50 yesterday to have his air-conditioner checked at an electronics repair shop in Williamsburg to make sure it would be ready for the heat. He took it home and turned it on. Only hot air came out. Now he was back in the shop, his blue polo shirt stained a few shades darker by sweat.

“The fan is useless,” Mr. Reyes complained in Spanish, pacing inside the graffiti-tagged warehouse of a store, where old A.C. units were piled outside. On a day like Saturday, as New York City and much of the country struggled to ride out a heat wave, Mr. Reyes saw his patience melt. “One cannot breathe properly without an A.C.,” he said.

New York roasted on Saturday as the heat approached 100 degrees, and thanks to air thickened by humidity, it felt even hotter. For some, the heat brought only discomfort. Yet officials feared far more perilous consequences. Mayor Bill de Blasio declared a state of emergency lasting through the weekend, saying in a news conference on Friday, “We have not seen temperatures like this in at least seven years.”