Tourists sheltered under umbrellas as they lined up at Florence’s majestic cathedral this week, looking for shade. Street vendors peddled fans and straw hats. Locals splashed their faces at water fountains, all seeking a respite from Europe’s latest heat wave.

“It feels like home,” said Alina Magrina, a 64-year-old tourist from California, parts of which, like much of the southern United States, have been hit by sweltering temperatures, too. “But at home, we move from one air-conditioned space to the next.” Walking in the sun in Florence was making her chest hurt, she said, stopping to buy an extra fan on the Italian city’s iconic Ponte Vecchio.

Extreme heat has now become a fixture of summer months in many parts of the world, not only in the United States, but especially in Europe, a continent defined by its almost immutable architecture and ways of life. Yet, though Europe is warming more swiftly than the global average, each year it seems particularly unprepared.

Experts say Europe’s governments have in significant ways failed to heed the alarms sounded nearly 20 years ago, when a heat wave in 2003, the continent’s hottest year on record, left 70,000 people dead by some estimates. A report published this week attributed 61,000 deaths in Europe to its searing temperatures last summer.

This year threatens to repeat the calamity. In some parts of southern Europe, heat waves started as early as May. The most recent heat wave — called Cerberus for the multiheaded dog that guards the gates of the underworld — tilted temperatures well above 37 degrees Celsius, or nearly 99 degrees Fahrenheit, in Florence, Rome and parts of Sardinia and Sicily this week.

Another round of high temperatures, part of the heat wave caused by an African anticyclone, is expected in the coming days, with peaks of 48 degrees Celsius, or 118 degrees Fahrenheit, or more.

Since the scorching summer of 2003, governments across Europe have put in place national adaptation strategies and regularly issued heat warnings and guidelines for residents. But they have also consistently missed carbon emission targets intended to slow climate change and failed to invest in tangible solutions.

“Europe unfortunately has not really used the time of the last 20 years well enough, to take the actions needed to reorganize cities,” said Benjamin Kötz, head of sustainable initiatives at the European Space Agency, which provides policymakers with satellite images that can help administrations plan climate resilience.

“But we have to be fair,” he added. “It is difficult because it comes with long-term planning and a lot of investment.”

Part of the problem is that much of the burden has fallen on municipalities, which have limited resources and limited avenues for heat mitigation in sometimes ancient urban spaces that are prized and protected from dramatic alterations.

Florence is as good an example as any of the impact of rising temperatures as well as the efforts at adaptation, and their limits.

This summer, like every summer, Florence, the cradle of the Renaissance, located in a wide valley where the Arno river historically facilitated trade, is one of the hottest cities in Italy. Last July, a month marked with uninterrupted high temperatures, Italy’s health ministry estimated a 34 percent increase in deaths in the city, in north-central Italy.

For nearly two decades, the city has been trying to adapt to the changing climate, refitting public offices, schools and hospitals, planting more trees and planning more parks in suburban areas. Yet Florence, like all Italian historical cities, has struggled in its attempts to make its centuries-old city center greener and cooler.

Sitting in his air-conditioned, frescoed office inside Palazzo Vecchio, the Florence city hall, Mayor Dario Nardella said that “much was done” since the early 2000s, but he added that there was “more to do.”

Florence’s hottest areas, mapped by the local university in the center and a northwestern neighborhood, share a number of features: they have almost no trees, and a lot of cement.

Mr. Nardella explained that the city has planted thousands of trees and invested almost a billion euros, or about $1.12 billion, to keep cars from the city center, building two new tramways to connect the peripheries with downtown.

When the first tramline in the city was built in 2010, the managing company even planted succulents between the tracks, following the principle that natural, permeable surfaces were cooler than asphalt.

Mr. Nardella showed a rendering of the planned renovation of one downtown street, where asphalt will be replaced with pietra serena stones and flanked with orange trees. It was one example, he said, but making changes in the historical center was hard.

“The national law to protect the cultural heritage is an obstacle,” Mr. Nardella said. “But so is our cultural identity and our history. Our cities have been like this for centuries.”

Experts agree that the modifications required for European cities to mitigate heat is daunting. “Europe has a lot of action plans, but the scale of changes required to adequately adapt to climate change is huge,” said Roop Singh, senior climate risk adviser at the Red Cross Red Crescent Climate Center.

She explained that, at the urban level, every building and home needs to be retrofitted to accommodate very high temperatures. Authorities would have to extend shelters and health services to poorer and more marginalized people, and to reduce so-called urban heat islands where temperatures are particularly high.

Urban adaptation experts generally agree that all sectors needed an overhaul, “from building to transport to health, agriculture, and productivity,” said Ine Vandecasteele, an expert at the European Environment Agency.

Governments need to involve all administrative levels also to address water shortages and flooding, which are other risks related to climate change. “Most countries are not aligned yet, but a lot of progress has been made,” she said.

Scientists in Florence and elsewhere in Italy are pushing to introduce cool pavements to lower the asphalt’s temperature and its heat-retaining capacity. Los Angeles has dozens of miles of cool paving, a technology almost unused in Italy.

“Decreasing cement in urban areas is not easy,” said Marco Morabito, a leading researcher at Italy’s National Research Council in Florence who has studied the issue of urban heat islands since the 1990s. “But there is a risk, considering the global trend, that buildings in the city centers will have critical living conditions for longer periods of time in the future.”

He explained that energy consumption for air conditioning will inevitably go up for residents in those districts as they try to cope with the extreme heat, and real estate will likely devalue. “The economic impact is more than we can think today,” Mr. Morabito said.

In a study published last year, the Bank of Italy noted that climate has an effect on real estate transactions, orienting purchasers or renters toward more climate-resilient buildings and lowering the prices for homes that are not shielded from the extreme heat.

The challenge is not Italy’s alone. Scientists believe that northern countries, even if less prone to very high temperatures, will have a harder time coping with them because people are less used to the heat. In 2010 in Moscow, thousands of people are estimated to have died during a heat wave.

Outside Italy, Mediterranean countries like Greece have started thinking about strategies to cope, but in those places, too, many of the efforts are local. The Greek authorities started using reflective pavement in the greater Athens area, but the consequences of the 2008 economic crisis made it impossible to scale up the project.

It took another decade for Athens to introduce a chief heat officer to coordinate measures to combat overheating at the city level.

Even countries along the Atlantic have taken smaller-scale measures. In the town of Cascais in Portugal, near Lisbon, the municipality tried to create space for water to filtrate into the ground, and it planted native species, which are better suited to adapt to water shortages, along the streets.

In Paris, the administration has started a program to transform schoolyards into green oases accessible to both students and local communities, creating a series of shelters open to everyone. The mayor has also pledged to make the Seine safe to swim ahead of an Olympic river race in 2024.

And in Copenhagen, local officials are removing parking lots, to discourage drivers from taking their cars into the city center.

Experts recognize that, in historical cities, some of the classic strategies to mitigate the heat won’t work. Habits like painting roofs white or making them with heat-reflecting roofing, mandatory in California, would be hard to imagine in a city like Florence, which imposes limits on the materials used to restore buildings in order to preserve the city’s historical character.

“Building materials like cool pavements have tremendously progressed in the past decade, but not the use of them,” said Mattheos Santamouris, a professor of high performance architecture at the University of New South Wales in Australia, and a global expert in smart urban design.

The cost of reducing the amount of carbon sent into the atmosphere from Europe is close to 260 billion dollars a year, he said, and, around the world, the annual cost of overheating will increase from 400 billions dollars to as much as 1.3 trillion by 2050.

“It is also a terrible discrimination because the first victims of extreme heat are poor people,” Mr. Santamouris said. “Ninety percent of those who died in 2003 were low-income people.”

In Lodi, a northern Italian city near Milan, a street worker collapsed this week as he was painting signs in heat of more than 104 degrees Fahrenheit. He later died in a hospital.