Most deaths have taken place in the southern states of Telangana and Andhra Pradesh, where more than 140 people have died since Saturday.
Allahabad in Uttar Pradesh recorded 48C while temperatures rose to above 44C (111F) in the capital, Delhi.
Authorities have urged people to stay indoors and drink plenty of fluid.
Heat wave conditions have been prevailing in the two worst-affected southern Indian states since mid-April, but most of the deaths have happened over the last week.
The Press Trust of India news agency said the heat wave had killed 186 people in 10 districts in Telangana state, with 58 people dying since Saturday.
In neighbouring Andhra Pradesh, the toll has risen to 182, with 87 deaths since Saturday.
“Almost all the victims are old…. Most of them were working and were exposed to the heat. Dehydration and heat stroke caused the deaths,” senior Telangana official BR Meena was quoted as saying by The Indian Express newspaper.
The meteorological department said the sweltering conditions were likely to continue for a few more days.
However, “no relief” is expected in Delhi for the next four days, and the “heat wave will continue,” an official said.
Reports said at least 10 people had died of the heat in the eastern West Bengal state.
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.
Meteorological officials said the heat wave was due to lack of rain.
