The Indian Meteorological Department said severe heat could stay for up to a week across Rajasthan, Maharashtra, Madhya Pradesh, Punjab, Haryana and Uttar Pradesh states.
Several deaths from heatstroke have already been recorded.
A red alert severe heat warning has been issued in the capital New Delhi as temperatures passed 46 Celsius, and residents were advised not to go out during the hottest hours of the day.
Even in the hill state of Himachal Pradesh, where many wealthy Indians go to escape the summer heat, temperatures reached 44.9 Celsius in Una.
Several major cities, led by Chennai, have reported fears of water shortages as lakes and rivers start to dry up.
In the western state of Maharashtra, farmers struggled to find water for thirsty animals and crops.
"We have to source water tankers from nearby villages as water reserves, lakes and rivers have dried up," said Rajesh Chandrakant, a resident of Beed, one of the worst-hit districts.
"Farmers only get water every three days for their livestock."With temperatures such as these, India draws perilously close to 'Wet Bulb 35.' That's when temperature and humidity combine to create conditions where the human body can no longer cool itself and begins to bake from the inside. That point is where the temperature reaches or exceeds 46 Celsius and the humidity reaches 50%.