When England chose their training base for this World Cup, they drew a latitudinal line across a map of the United States.

They knew that everywhere south of the line would have temperatures too high for the players to train every day, during what was expected to be the hottest World Cup since 1994. But they did not want to go too far north, either. They needed somewhere hot enough to acclimatise the players.

This question of heat has hung over England’s preparations for this World Cup like no other. Thomas Tuchel attended the Club World Cup here last summer, and looked into what it took for a European team to win. Anthony Barry, his assistant coach, spoke about developing a “heat-proof game model” that could work in North America. England flew straight out to Florida, as early as they could, to get the players used to it, comfortable with being uncomfortable.

And then England played their first game in Dallas on Wednesday and produced something close to their natural game. The way they cranked up the intensity in the second half against Croatia looked like a Premier League game, in a way that you rarely see in international football. This is what Tuchel had promised he wanted to see from his England side. But it was not what many people expected at this World Cup, which felt like it might be even more dominated by low blocks, counter-attacks and set pieces than recent international tournaments.

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But by the end of the game, according to FIFA’s own statistics, England’s players had covered 117km. Only eight of the 47 other nations ran more than that over the first round of fixtures. England’s players completed 6.6km in what FIFA terms ‘Zone 4 sprints’, between 20-25kph (12-15mph). Only four teams — France, Jordan, Brazil and Austria — recorded more. It was an impressive physical effort, allowing England to impose their game on Croatia precisely how they wanted.

Here, it must be remembered that England were playing at AT&T Stadium on Wednesday, under the giant roof in air-conditioned surrounds that are kept steady at around 22C (72F). They were not exposed to the full extent of the Texan sun, with temperatures outside reaching around 34C. They may not have been able to outrun Croatia quite like this if they had.

But that does not mean it was easy. It was humid under the roof and the effort took a huge amount from the players. Many looked physically and emotionally tired at the end, as they gathered in front of the end full of England fans singing Wonderwall.

“Some players suffered because it was quite hot and humid, and the game was very intense,” Tuchel said afterwards. “That would be no surprise.” He went on to say that John Stones, whose first-team football was limited at Manchester City last season, “had cramps in both legs in the end because it was intense”.

Dallas’ stadium is air-conditioned but England will have to adjust to higher temperatures later in the World Cup (Michael Steele/Getty Images)

Tuchel had seen the players’ physical output stats post-game and was impressed, especially given the conditions. “They really put a shift in. The players said it was quite humid and difficult to digest it. Everyone was very tired in the dressing room, which I like because then you know that you did something. And we need this.”

The challenge, of course, is whether England can play like this in Foxborough and New Jersey next week against Ghana and then Panama. Neither of those stadiums has the same air conditioning that they found in Dallas. Foxborough, perhaps fortunately for England, is forecast to be warm (around 24C) and wet when England play there on Tuesday afternoon. New Jersey is likely to be warmer (27C) and wetter. So perhaps in the immediate term, it will be less of an issue.

But England are in pole position to win the group and if they do, their path will take them through Atlanta, Mexico City and then Miami in the quarter-finals. Atlanta has an air-conditioned stadium but Miami does not. Temperatures there can easily push well into the mid-30s, with oppressive humidity adding to the discomfort.

England can take comfort from their time in Florida before the tournament began. Jordan Henderson was asked at a press conference at England’s Kansas City base on Sunday whether they would be able to press the way they want to in the American heat. Henderson said that England would want to play “high intensity” football, but pointed to their 3-0 win against Costa Rica in Orlando on June 10.

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Henderson, who has a long international career behind him, said it was the best pre-tournament friendly performance he has seen. “I thought it was high level, and it was hot and humid,” he said. “I felt the performance was very good, and that physically we looked very good.”

Tuchel also pointed back to that Costa Rica friendly after the Croatia match, especially how his substitutions allowed England to maintain the physical pressure when other players were starting to tire. He knows as well as anyone what a physical slog this World Cup will be, with up to eight games, a multitude of flights and time-zone changes to navigate over five weeks.

“It is the only way,” Tuchel said. “I was so impressed with everyone against Costa Rica, because they pushed on the buttons, pushed on the gas, and kept suffocating the opponent. We needed this quality today to bring it over the line.”

Now Tuchel will hope that England can keep on pushing those same buttons for another long, draining 90 minutes in the heat in Boston next Tuesday.