Two of the first round of matches at the World Cup were played at a level of severe heat that a football players’ union has previously said should trigger the delay or postponement of games, a Guardian analysis has found.

A further four games were played in cities with temperatures also beyond that level of heat, though conditions inside the stadiums were mitigated by air conditioning.

Saudi Arabia’s game against Uruguay in Miami had the most severe heat conditions in the analysis of the first 24 matches of the World Cup, ie each team’s first game, in the tournament being held across the US, Mexico and Canada. The second most severe heat conditions of the first 24 matches in stadiums without AC were in Sweden v Tunisia in Monterrey.

These games, despite being evening kick offs, were played amid wet-bulb temperatures of 28C (82F) or above, according to temperature and humidity data for the place and time of the games.

Fifpro, the global players’ union, has previously argued that games played at 28C or above should be delayed or postponed. Asked about the Guardian analysis, the union declined to comment on the heat situation at the World Cup. This tournament is forecast to be the hottest such tournament to be held since the quadrennial competition began in 1930.

Wet-bulb temperatures are a measure of heat stress that combines air temperature, humidity and cloud cover to determine how well a human body can cool itself through sweating. Beyond a certain level of heat and humidity, sweat is unable to evaporate properly, leading to swift overheating that can result in illness or even death.

The Guardian used weather data from government agencies in the US and UK and derived the wet-bulb temperatures from a formula used by authorities in several countries, including Australia and Canada.

Faced by the prospect of a roasting North American summer, Fifa has moved some kick-off times to later in the day and introduced mandatory water breaks. A handful of the 16 World Cup venues have roofs or air conditioning that has ameliorated some of the high temperatures.

On Wednesday, for example, England played Croatia in Dallas in the fiercest wet-bulb temperatures to date at nearly 35C (95F), although the air conditioning inside the stadium brought this down to a more reasonable 22C (71F).

In total, six of the first 24 matches have been held in places where the wet-bulb temperature hit 28C or above – Germany v Curacao in Houston, Saudi Arabia v Uruguay in Miami, Portugal v DR Congo in Houston, the Netherlands v Japan in Dallas and England v Croatia, also in Dallas. The stadium in Houston also has air conditioning.

Record-high temperatures in some places resulted in some fans wilting in shadeless heat, with warnings that stadium workers, who often have to toil long before games with heavy equipment, are facing potentially hazardous conditions.

Current Fifa guidelines state that cooling breaks should take place if games are held in heat of 32C (89F) or above – in practice, these drinks breaks have occurred at lower temperatures at this World Cup – with delay or suspension of games at the discretion of competition organizers.

On the eve of the World Cup, a group of heat and public health experts urged Fifa in an open letter to implement more extensive heat protections, citing Fifpro’s call for games to be potentially called off if they reach 28C or above.

“Temperatures are often taken from shaded areas and if players are in direct sun, it can be double figures more than the temperature readings,” said Robbie Parks, an environmental epidemiologist at Columbia University and a signatory of the open letter. “Standing in the sun can be dangerous even at lower temperatures, even above 23C (73F) or 25C (77F) would make me concerned for older adults out there for more than few minutes.”

Parks said that air conditioning, later kick-off times and water breaks will help players, but that further measures are needed for fans and workers. “Shade is super important and hydration is super important,” he said.

“You need to allow people to bring in their own water and think about having misters for evaporative cooling. The final is going to be held in New Jersey, and that stadium isn’t covered which makes me worry. But I’d hope Fifa will learn the best way to deal with that by then.”

Extreme heat is the deadliest hazard worsened by the climate crisis, causing more deaths each year than hurricanes, floods and wildfires combined. The World Cup tournament itself is set to add to the planet-heating pollution that is causing worsened heatwaves around the planet, with the staging of more than 100 matches expected to result in 7.8m tonnes of greenhouse gases, double the amount of the previous World Cup in Qatar, according to estimates by Greenly, a global carbon accounting platform.

A Fifa spokesperson said the governing body is “committed to protecting the health and safety of all players, referees, fans, volunteers and staff” at the World Cup. Fifa has stationed meteorologists at match venues to assist on preparing for extreme weather and that tournament planning includes “close coordination” with host city organizers as well as stadium authorities and national agencies.

Ahead of the tournament, Fifa agreed a “tiered mitigation model” for extreme temperatures, with added interventions kicking in at different thresholds. For players, alongside mandatory hydration breaks, there is access to water and electrolyte drinks as well as other cooling tools including ice, cold towels, fans, mist and shade.

For spectators, elevated temperatures mean match stadiums will “activate additional cooling capacity, including shaded areas, misting systems, cooling buses and expanded water distribution”, the Fifa spokesperson said.

A medical set-piece protocol for the treatment of heat exertion has also been introduced, with cooling bags set to be used for the first time.

Fifa added it will “continue to monitor conditions in real time, integrating wet bulb globe temperature and heat index surveillance, and stands ready to apply established contingency protocols should extreme weather events occur”.