The heat index at Chicago O’Hare International Airport peaked at 101 degrees Fahrenheit on Monday, and the National Weather Service warned that the thermometer would only creep higher this week as furnace-like temperatures that have gripped much of the central United States spread east.

City and county officials across the country have opened cooling centers and urged people to take seriously warnings from meteorologists that tens of millions of people are at risk for what the Weather Service called “dangerous” high temperatures. Hundreds of daily record temperatures could fall by next week, they said.

In Philadelphia, officials shortened the length of a parade scheduled for Friday ahead of Independence Day. In Ohio, Gov. Mike DeWine urged people to check on their neighbors. In New York, Mayor Zohran Mamdani set in motion what he called an “unprecedented, historic heat emergency plan.”

Key things to know about the heat wave:

• The heat will spread east and linger for days. Forecasters warned many places will experience multiple days of high temperatures with little relief at night. Heat index values — a measure of what the temperature feels like to the human body, when humidity is considered with the air temperature — could reach as high as 110 to 115 degrees.

• While tying a single heat wave to climate change requires analysis, scientists have no doubt that heat waves around the world are becoming hotter, more frequent and longer lasting.

• Heat is the leading cause of weather-related deaths in the United States. Here’s what it does to your body, and here are tips to stay cool.

The day-by-day forecast:

Tuesday

Heat has been building across the Plains since Sunday, and on Tuesday it will become more intense, especially around the Great Lakes. It will also begin to spread farther east, across Ohio and into western Pennsylvania and New York, and farther south, into Tennessee and Missouri.

More than 100 million people are under an extreme heat warning on Tuesday. This number will grow as the week goes on.

Chicago’s Office of Emergency Management said it had opened cooling centers in the city and had begun sending outreach teams to help people without homes find respite from the heat this week.

Overnight temperatures in the Chicago area will be in the high 70s through much of the week, said Casey Sullivan, a meteorologist with the Weather Service. Heat indexes in the city could remain in the 90s until midnight or later.

These conditions do not “really allow for any cooling,” Mr. Sullivan said.

Wednesday

Once again, places that were already hot will become hotter, and higher temperatures will spread farther east. By Wednesday, most of the East Coast will be at some risk of dangerous temperatures, according to the Weather Service, but the most extreme temperatures will remain in the states around the Great Lakes.

Most of Wisconsin, Ohio, Michigan and Illinois will be under the service’s most extreme and rare warning level, reserved for long-lasting extreme heat that offers little to no relief at night.

Washington, D.C., could reach 100 degrees for four consecutive days between Wednesday and Saturday — with the potential to tie a record for the city, said Michael Muccilli, a meteorologist with the National Weather Service.

In New York, the heat index could climb above 100 degrees on Wednesday, Thursday and Friday. The city’s mayor, Zohran Mamdani set in motion what he called an “unprecedented, historic heat emergency plan.”

Thursday

The worst of the heat is forecast to reach much of the East Coast by Thursday. But areas around the Great Lakes are not likely to see a respite.

Some 250 million people — from the Dakotas to Boston and south to Miami — live in areas that are expected to experience some level of dangerous heat on Thursday, according to the Weather Service.

Cities including Washington, New York, Philadelphia and Boston could see temperatures climb into the low 100s, with several daily records under threat. Forecasters said Philadelphia could also tie its all-time June record high of 104 degrees.

Periods of prolonged, persistent heat are among the deadliest weather hazards in the United States because the effects build over time. The consecutive hot days and warm nights will prevent the body from fully recovering.

Friday

Friday looks a lot like Thursday, which means little relief for some places that will have had four or more days of extreme temperatures. It may be the hottest day of the week in some areas like New York City.

There is some chance of afternoon and evening thunderstorms that could provide some temporary relief on Friday and Saturday across the Northeast, but most places are likely to stay hot and dry.

Fourth of July and the Weekend

The heat is likely to peak on the East Coast by Saturday, but high temperatures are still expected to stick around into early next week before really subsiding, Mr. Muccilli said.

In Philadelphia, where temperatures could reach 100 yet again, a World Cup match is set to kick off at 5 p.m. on Saturday.

By Sunday, many of the most extreme heat warnings will have passed, but dangerous heat is likely to remain across parts of the Washington metro area, Virginia and the Carolinas.

How to stay cool:

Staying cool and hydrating often are two of the most important things you can do in extreme heat.

Andy Newman, Camille Baker and Julie Bosman contributed reporting.