The heat dome that smashed all-time records in the northern Rockies and Northern Plains is now spreading searing heat and humidity across the Midwest and then the East.

(MORE: What is a heat dome?)

Historic heat records were tied or broken

This heat wave already rewrote the history books in parts of four states on Sunday.

Montana's largest city, Billings, topped out at 111 degrees, easily topping their previous all-time record of 108 degrees.

Miles City, Montana, soared to 115 degrees, obliterating their previous record of 111 degrees and just 2 degrees shy of the state's all-time record and the high in Death Valley's Stovepipe Wells Sunday.

Salt Lake City also had its hottest high in over 150 years Sunday, topping out at 109 degrees.

Elsewhere, Sheridan, Wyoming (109), and Idaho Falls, Idaho (103) broke their all-time records, as well.

(CURRENT MAPS: Temps | Heat Index)

Heat alerts

The map below shows where the National Weather Service has issued heat alerts, including extreme heat watches, warnings and heat advisories, stretching from the Northern Plains to New England and the mid-Atlantic states.

An extreme heat watch is issued when conditions are favorable for an extreme heat event that could lead to heat-related illnesses, including heat exhaustion and heat stroke, within the next 24 to 48 hours. Watches are upgraded to warnings when those conditions become more certain.

This is the time to plan to suspend all major outdoor activities if a warning is issued. If you do not have air conditioning, locate the nearest cooling shelter or discuss staying with nearby family or friends who have air conditioning.

(MORE: 5 things to know to stay safe in a heat wave)

Midwest, Northeast heat forecast

The hot, humid air mass will spread from the Midwest to the East by Tuesday.

How hot will it get?

Many of these areas will see temperatures soar into the 90s by the afternoon. A few areas in the Midwest and East Coast could approach 100 degrees around the middle of the week.

This could set some daily records Tuesday and Wednesday in parts of the Northeast from New England and upstate New York to the mid-Atlantic states.

Morning lows, especially in larger cities, may languish in the middle or upper 70s, offering little evening or nighttime relief.

(MORE: America's deadliest weather is heat, not tornadoes or hurricanes)

When will relief arrive?

A fairly strong cold front is forecast to plunge out of eastern Canada into the northern tier of states later Tuesday into Wednesday. A secondary cold front will follow right behind the first later this week.

That could bring some heat relief from the northern Great Lakes to northern New England by Wednesday, then to more of the Midwest and Northeast starting Friday into the weekend from north to south.

(MAPS: 10-day US forecast highs and lows)

West heat forecast

In general, any heat relief in the Rockies and Northern Plains this week will be subtle.

We won't see the top end all-time record heat of last Sunday repeated, but highs in the 90s will be common much of this week in lower elevations of the Northern Plains and Rockies.