A blanket of steamy, hot air has gripped Quebec and much of central and eastern Canada since Saturday.
Environment Canada advises that extreme heat affects everyone.
"We go out to the paramedics, we go out to the hospitals and we ask them to make sure to identify any deaths they believe are related to heat and that allows us to intervene more quickly", Kaiser said.
Sudbury has been under a heat warning since Friday. Daytime temperatures will again be near 30 degrees, with humidex values in the mid 30s.
"It could save a life", Genereux said.
"None of the people we've identified in the last four days had air conditioning at home", Kaiser noted.
Montreal city hall unveiled an "extreme heat" plan on Tuesday that includes distributing water to groups working with the homeless.
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Meanwhile, public-health officials in Quebec's Eastern Townships report four deaths suspected of being caused by the heat; one victim was a senior citizen and three were adults suffering from chronic illnesses.
"My thoughts are with the loved ones of those who have died in Quebec during this heat wave", Prime Minister Justin Trudeau said on Twitter.
Montreal's civil services have announced the introduction of measures aimed at ensuring the well-being and safety of residents, including a door-to-door operation created to reach at-risk people and to provide prevention advice in certain areas.
Heat warnings are issued by Environment and Climate Change Canada to inform the public when air temperature and humidex are forecast to be above a certain criteria for two consecutive days.
Urgences-sante president Nicola D'Ulisse says the service is overwhelmed and has reached the limits of what it can provide.
He is asking residents to call a provincial health-consultation line in the event of minor health problems or to check in with friends or family and leave 911 lines free for real emergencies.