The worst-hit state was Andhra Pradesh on the country's southeast coast, where 42 people have died in the past 24 hours. The total toll in that state is now 1,719, according to K. Dhananjaya Reddy, director of the state's disaster management.
At least 585 have died in the neighboring landlocked state of Telangana, and 26 in Odisha, farther north.
Temperatures hit a high of 48 degrees Celsius in some cities last week -- that's 118 degrees Fahrenheit.
It's been cooler in recent days, but officials are only now determining how many people succumbed to last week's unusually hot weather.
On Monday, the country's highest maximum temperature -- of 45.4 C or 113.7 F -- was recorded at Daltongan in Jharkhand state. Heat wave conditions remain in isolated areas of that state, as well as some areas of Bihar.
Elsewhere, thunderstorms have cooled several parts of India, including coastal regions of Andhra Pradesh.
Monsoon rains had been forecast to hit the country's southern coast on June 1, but forecasters say they're not likely to arrive until Friday.
According to an official statement from the India Meteorological Department, "persistence of convection indicates that conditions are becoming favorable for the onset of southwest monsoon over Kerala around 5th June."
A week ago, it was hot enough in Delhi, in the north, to melt roads.
People are trying to stay cool in whatever way they can. The government is urging residents to use an umbrella, hat or turban to protect themselves from the sun -- and drink plenty of water.
"Cover properly, have light-color clothes, take umbrella, take care, be in cool area," said B.R. Meena, the chief secretary of Telangana. He also urged residents to stay out of the sun during the hottest parts of the day, from 11 a.m. to 4 p.m.
Meena said if the heat wave victims "had they taken such care, this could have been avoided."
Many of those who have succumbed to heat are poorer members of society and the homeless who had nowhere to go.
Throughout Hyderabad, water camps opened, providing free water to anyone who needed a drink.
The poor and ill affected most
Temperatures dipped at night, but even then it was uncomfortably hot. On Wednesday night last week, men slept on footpaths and on concrete strips between roads in temperatures of up to 37 C, or 98.6 F.
Two old men were seen sleeping under a flyover, as cars sped by spewing even hotter, polluted air in their direction. Construction workers stretched out on top of huge steel pipes.