The figure marked an increase of 13 from a week earlier, although not all the additional deaths happened in recent days but instead reflected delays updating the data.
Last year, Mexico reported a record 419 heat-related deaths in the hot season, which runs from March to October, in a country of 129 million people.
President Andres Manuel Lopez Obrador has described this year's heat as "exceptional."
On Saturday, Mexico City recorded its highest-ever temperature of 34.7 degrees Celsius (94.5 degrees Fahrenheit), according to the National Meteorological Service.
The capital, which sits at 2,240 meters (7,350 feet) above sea level, has traditionally enjoyed a temperate climate but has not been spared from this year's heat waves.
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