Paris wanted a green Olympics. Team USA wants air conditioning.

There was, however, one deliberate oversight. The organizers of the Summer Games, in their efforts to be friendlier to the environment, chose not to install air conditioning.

For much of the world, a few fitful nights of sweating in front of open windows is simply a reality of summer. But some Olympians are more reliant on climate control than others—namely the members of Team USA.

They are now discovering what generations of American tourists have encountered on their European vacations: When you ask for A/C in France, you’re more likely to receive a giant Gallic shrug.

“We appreciate the concept of not having air conditioning due to the carbon footprint," Australian Olympic committee chief executive Matt Carroll told reporters. “However, it is a high-performance Games. We’re not going for a picnic."

That’s not to say organizers are letting athletes slow-broil for three weeks. The Village here, located just north of Paris, was built with a cooling system that runs cold water through the floors, which officials say can reduce the ambient temperature by 10 to 20 degrees Fahrenheit and achieve a target range of 73 to 79 Fahrenheit. The effort is part of the hosts’ larger plan to make Paris the greenest Olympics in modern history, which includes measures such as reducing the number of vehicles by 40% from previous Games, building fewer new venues, and cutting the Games’ carbon footprint by half compared with the average of London 2012 and Rio 2016.

But for those athletes who remain unconvinced and worry about their performance being derailed by sleeping in sweatbox apartments, Paris 2024 has made air conditioning units available for hire. And there are no gold medals for guessing which delegation leads the way.

The 592-strong Team USA delegation isn’t risking the slightest discomfort. Every single U.S. room and some common areas have been equipped with portable A/C units, according to a spokesman for the U.S. Olympic & Paralympic Committee. The Americans will all be able to take on any Paris heat wave by hanging out in meat-locker conditions, even though temperatures over the next 10 days aren’t expected to top 90.

Still, Team USA isn’t alone in requesting the option to refrigerate itself. Out of the 7,000 rooms in the Village, 2,500 have been supplied mobile air conditioning units at the teams’ requests, a Paris 2024 spokesman said.

“For what is often the biggest competition of their athletes’ lives, certain National Olympic Committees have chosen to equip themselves with additional mobile air conditioning units," the spokesman continued. “These appliances are at their own cost, and Paris 2024 is offering support by proposing air conditioners that will subsequently be made available to Paralympic athletes."

Keeping cool at all times is that much more important given the erratic schedules that some of the athletes here are facing, said Carroll, the Australian Olympic committee executive. Since many athletes’ events are at night, they’ll need to sleep during the hottest part of the day. So the decision to pay for air conditioners was a no-brainer.

“Most will only live the Games once," said Brice Guyart, a former Olympic fencer who is responsible for the athlete experience at Paris 2024. “So we have to give them a crazy good experience."

But not everyone is all-in on A/C. Germany’s Olympic sports federation will have one of the larger contingents in the village with around 350 athletes. That includes 6-foot-7½-inch decathlon medal favorite Leo Neugebauer, who recently won the NCAA title competing for the Texas Longhorns in Austin, where air conditioning isn’t merely a suggestion—it’s a way of life.

When Germany asked its individual sport federations if they wanted to order air conditioning units for the athletes’ village, demand for frigid air was lukewarm, according to Olympic committee spokesman Michael Schirp.

“A total of 11 AC have been ordered. Eleven," he wrote, adding an emoji of a face wearing sunglasses.

Schirp later pointed out that the Germans reserve the option to change their minds should Paris suddenly begin to bake like a croissant oven.

“When we get [104 degrees] in the second week, we can call again," he joked. “Send us some AC!"

Write to Rachel Bachman at Rachel.Bachman@wsj.com and Joshua Robinson at Joshua.Robinson@wsj.com