The oppressive heat wave that has the southern United States sweltering this week is expected to continue, spreading north and east to parts of Louisiana, Arkansas, Mississippi, Alabama, Missouri, Tennessee, Georgia and Florida, and is threatening to raise the heat index to dangerously high levels in places, according to the National Weather Service.

Temperatures are expected to be up to 20 degrees above normal, reaching the upper 90s or low 100s in some parts, with nighttime temperatures offering little respite, and high humidity continuing to produce “potentially life threatening” heat through the rest of the week, forecasters said. “It is essential to have ways to cool down and limit your heat exposure,” the Weather Service warned on Twitter on Tuesday evening.

The worst impacts are expected in eastern Texas, along the Central Gulf Coast and through parts of the Mississippi and Tennessee valleys, where the heat index could reach between 110 to 120 degrees in major cities including Dallas-Fort Worth, San Antonio, New Orleans, Little Rock, Jackson, Memphis, Montgomery and Nashville.

The heat index is a measure of how hot it really feels, when humidity and other factors are considered along with the temperature. When the index goes over 103 degrees, experts label it as dangerous heat. Such temperatures carry a higher risk for cramps and exhaustion as well as heat stroke, particularly after exercise or long stretches in the sun.

Parts of Northern California — where cool weather and gloomy skies have reigned for several weeks — will also begin to get hotter from Thursday, with much of Sacramento and the San Joaquin Valley already under excessive heat warnings, the Weather Service said. Though temperatures are not expected to be above average in the Southwest, dry conditions and low humidity, combined with gusty winds, will increase fire danger across much of Arizona, New Mexico and southwestern Texas.

Already, the excessive heat has killed three hikers, brutalized workers and caused spikes in ambulance calls and emergency-room visits, as cities caution residents to stay indoors and drink water. As of Tuesday evening, more than 61 million people were under excessive heat warnings or advisories, according to data from the National Weather Service.

The unusually hot, early summer temperatures are the result of a stubborn “heat dome” of high pressure (akin to a lid on a pot that holds in steam). Forecasters have warned that the relentless heat could continue across much of the South through the weekend.

The heat will persist next week, with parts of the Great Lakes, Midwest, Idaho and eastern Washington State expected to be up to 10 degrees above normal, said David Roth, a meteorologist with the Weather Prediction Center of the National Weather Service.

“This may be outside of what you would normally expect in summer,” Mr. Roth said. “Prepare for that.”

John Keefe contributed reporting.