Thirty-three people have died in Quebec from one of the worst heat waves to hit eastern and central Canada in decades, say authorities.

On Thursday, as temperatures in Montreal rose to 33.8C, residents sought refuge in park fountains or remained inside in air-conditioned homes or offices. Some elderly residents cancelled medical appointments and stayed at home, eager to avoid the stifling heat outside.

Dr David Kaiser, the senior physician at Montreal’s public health agency, said that most of those who had died from the heat in Montreal were 65 or older, had histories of health problems or mental illness and had been living without air-conditioning.

He said that disadvantaged people who had chronic illnesses or were living alone were particularly vulnerable.

“While we are an advanced industrialised economy, these deaths reflect that there are serious social inequalities,” added Dr Kaiser.

Public health authorities in Quebec have made a concerted effort to improve the reporting of heat-related deaths, establishing a special liaison program with hospitals and emergency rooms to monitor heat-related illnesses and mortality.

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Dr Kaiser believes this could explain why the number of deaths seems high compared to elsewhere in Canada.

Home appliance stores have been mobbed in recent days, with residents trying to buy air-conditioners, only to discover that all the units are sold out. At a sprawling Home Depot store in central Montreal, about 20 shoppers were seen fighting this week over the last remaining air-conditioner. “It’s survival of the fittest,” said Victor Perchet, who managed to get it.

Environment Canada has issued a heat warning for southern Quebec, much of Ontario, New Brunswick and Nova Scotia. To protect themselves against the heat, it called on residents to drink six to eight glasses of water a day, to avoid alcohol, to spend at least two hours a day in air-conditioned or cool places and to avoid leaving children or babies alone in sweltering vehicles.

Prime Minister Justin Trudeau took to Twitter to warn people to be vigilant. “My thoughts are with the loved ones of those who have died in Quebec during this heat wave,” he wrote. “The record temperatures are expected to continue in central & eastern Canada, so make sure you know how to protect yourself & your family.”

Police and firefighters in Montreal visited 15,000 homes this week to check on elderly residents.

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The emergency services in Montreal say there has been a sharp increase in calls since the heat wave began - a total of some 1,200 calls a day.

Mayor Valerie Plante of Montreal has called on the city to come together to protect against the heat, including knocking on neighbours’ doors “just to find out if the person is O.K.”