MADISON, Wis. — Tens of millions of people across the Midwest and East braced Sunday for another sweltering day of dangerously hot temperatures as a rare June heat wave continued to grip parts of the U.S.

Most of the northeastern quadrant of the country from Minnesota to Maine was under some type of heat advisory Sunday. So were parts of Arkansas, Tennessee, Louisiana and Mississippi, the National Weather Service said Sunday.

Sunday marked the second straight day of extreme heat across the Midwest and East Coast. Heat indices on Saturday hit 103 Fahrenheit in Chicago and 101 in Madison, Wis., turning that city’s annual naked bike ride into a sticky and sweaty affair.

Lynn Watkins, 53, is the director of Sacred Hearts Day Care in Sun Prairie, a Madison suburb. She said that she tried to sit outside Saturday to grill but it was so hot she had to go inside. She plans to cancel all outdoor activities at the day care on Monday with highs around 93 forecasted.

“I can’t stand being outside when it’s like this,” she said. “I just want to sit in my air conditioning.”

The temperature reached 80 in the Chicago area by 7:30 a.m. Sunday. Forecasts called for heat indices of between 100 and 105.

The heat index in Pittsburgh was expected to top 105. The temperature in Columbus, Ohio, was 77 at 8:30 a.m. Highs there were expected to reach 97 with a heat index around 104.

Forecasts called for a heat index of 100 in Philadelphia on Sunday, with a 108 heat index on Monday.

The city’s public health department declared a heat emergency starting at noon Sunday and ending Wednesday evening. Officials directed residents to air-conditioned libraries, community centers and other locations, and set up a “heat line” staffed by medical professionals to discuss conditions and illnesses made worse by the heat. At Lincoln Financial Field, officials said each fan attending Sunday’s FIFA World Cup match would be allowed to bring in one 20-ounce plastic bottle of water.

Forecasters warned the heat index in Cromwell, Connecticut, would reach 105 on Sunday, which could make life brutal for golfers Tommy Fleetwood and Keegan Bradley as they compete during the final round of the Travelers Championship.

Cincinnati Reds shortstop Elly De La Cruz, playing against the Cardinals in St. Louis, and Seattle Mariners reliever Trent Thornton, facing the Cubs in Chicago, got sick Saturday while playing in the extreme heat.

Meteorologists say a phenomenon known as a heat dome, a large area of high pressure in the upper atmosphere that traps heat and humidity, is responsible for the extreme temperatures.

Mark Gehring, a National Weather Service meteorologist in Sullivan, Wisconsin, said this level of heat is not uncommon during the summer months in the U.S., although it usually takes hold in mid-July or early August. The most unusual facet of this heat wave is the sheer amount of territory sweltering under it, he said.

“It’s basically everywhere east of the Rockies,” he said, referring to the Rocky Mountains. “That is unusual, to have this massive area of high dewpoints and heat.”