At least 650 bodies have been brought here since Saturday. Many lie in storage. But an oppressive heat wave -- and the frequent power outages from electricity grids trying to keep up with demand -- means the morgue is unable to properly maintain the temperature at the overcrowded facility.

A handwritten sign outside says the morgue is filled to capacity. Other bodies lie outside.

Such is the state of affairs in the beleaguered seaport city of Karachi. A record-breaking heat wave has killed 800 in the city and 38 others elsewhere in Sindh province, according to the chairman of Pakistan's National Disaster Management Agency, Gen. Asghar Nawaz. Authorities fear the toll will only rise.

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The Rangers, Pakistan's paramilitary force, have set up 10 relief centers across the city, distributing water and salt tablets. But even that has proven inadequate.

Ambulance after ambulance arrives at Karachi's Jinnah Post Graduate Medical Center with a steady stream of victims suffering from dehydration and heat exhaustion.

Over the past four days, between 7,000 and 8,000 people have been treated in that hospital alone, the majority suffering from heat stroke, said Seemi Jamali, a senior official at the medical center.

Some of the patients brought in had been found collapsed in the street, Jamali said Wednesday.

Throughout Sindh province, the local government has canceled leave for medical personnel and brought in extra help to deal with the onslaught of patients.

Brutal heat wave

The city is used to baking in the heat around this time of the year, just before the monsoon rains arrive as welcome relief.

But this year's heat wave has been particularly brutal.

It began Friday. On Saturday, temperatures reached 44.8 degrees Celsius (112.64 degrees Fahrenheit) -- the highest-recorded temperature in the country in the last 15 years.

Sunday's temperature dipped slightly to 42.5 Celsius (108.5 F).

Cooler temperatures are expected to arrive later in the week.

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Ramadan obligations add pressure

The heat wave comes at a time when the citizens in this predominantly Muslim country are observing Ramadan. During the holy month, the faithful fast from sunup until sundown.

This means that, amidst these scorching temperatures, Pakistanis are forgoing food and water.

Certain segments of the population, however, are excused from fasting, such as the elderly and the infirm.

Making matters worse, Karachi is dealing with frequent power outages as the electricity grids are unable to keep up with the demand in the city of 16 million.

Jamali, the hospital official, said that a lot of patients who were brought in had fallen ill because they had gone without power for so long.

To the east, a heat wave struck Pakistan's neighbor India last month, killing more than 2,000 people.

CNN's Sophia Saifi reported from Karachi, and Euan McKirdy wrote from Hong Kong. Journalist Zille Hyder and CNN's Jethro Mullen contributed to this report.