Most deaths have taken place in the southern states of Telangana and Andhra Pradesh, where more than 140 people have died since May 23.
Allahabad in Uttar Pradesh recorded 118°F while temperatures rose to above 111°F in the capital, Delhi.
Authorities have urged people to stay indoors and drink plenty of fluids.
Heat wave conditions have been prevailing in the two worst-affected southern Indian states since mid-April, but most of the deaths have happened in the past week.
The worst-hit state has been Andhra Pradesh where 246 people have died from the high temperatures in the past week. State officials said 62 people died of sunstroke on May 24.
Residents of Nalgonda in newly-formed state of Telangana are used to high temperatures during the summer months.
The Press Trust of India (PTI) news agency said the heat wave had killed 186 people in 10 districts in neighboring Telangana state, with 58 people dying since May 23.
The north-western desert state of Rajasthan has also recorded several deaths due to the heat, the PTI reported, including a woman who collapsed and died on a roadside in Bundi city.
The meteorological department said the sweltering conditions were likely to continue for a few more days.
At least 10 people had died of the heat in the eastern state of West Bengal, reports say.
Non air-conditioned taxis will be taken off the road for five hours during the day in the main city in the state capital, Kolkata, after two drivers died from heat stroke.
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