Dr. Yadav put Rehmati, who is 31 and goes by one name, on a drip. She held her hand and told her she would be fine. Rehmati leaned over and retched.

Extreme heat can kill, as it did by the dozens in Pakistan in May. But as many of South Asia’s already-scorching cities get even hotter, scientists and economists are warning of a quieter, more far-reaching danger: Extreme heat is devastating the health and livelihoods of tens of millions more.

If global greenhouse gas emissions continue at their current pace, they say, heat and humidity levels could become unbearable , especially for the poor.

It is already making them poorer and sicker. Like the Kolkata street vendor who squats on his haunches from fatigue and nausea. Like the woman who sells water to tourists in Delhi and passes out from heatstroke at least once each summer. Like the women and men with fever and headaches who fill emergency rooms. Like the outdoor workers who become so weak or so sick that they routinely miss days of work, and their daily wages.