Forecasters advised people to stay hydrated and find places to cool off, warning of temperatures eight to 14C warmer than normal in many areas, including at night - especially bad for people's health because their bodies won't have a chance to recover.
The heat dome was expected to affect as much as two-thirds of the continental United States.
"The heat doesn't necessarily stop when it's dark out," said Josh Adam, a meteorologist with the National Weather Service in Bismarck, North Dakota, where temperatures will surpass 37C until Tuesday, a dramatic spike for the state.
The National Weather Service predicted that more than 90 US local temperature records will be tied or broken through Wednesday - with two-thirds of those being overnight heat records.
Temperatures were not forecast to drop below 27C at night in Fort Lauderdale, Florida; Miami; Tampa, Florida; Galveston, Texas; and Charleston, South Carolina.
The heat dome - formed when high pressure traps hot air while blocking cooling winds and rain - is one of the strongest to affect the Dakotas in 25 years, said Chad Merrill, a senior meteorologist with AccuWeather.
Record highs were forecast for the weekend in Nevada, Utah, Colorado, Wyoming, Idaho, Montana and the Dakotas.
Nevada, a state accustomed to hot weather, was even hotter than normal, said Andrew Gorelow, a meteorologist with the National Weather Service in Las Vegas. The temperature there was expected to hit 48C on Saturday, Gorelow said.
They also warned that the heat could spike fire risk in some parts of the country that already are dry, including the Rockies, where Merrill said dry thunderstorms could develop.
Climate change is causing more intense and longer-lasting heat waves that cover larger areas, scientists say.
This year's temperatures also are expected to be affected by El Nino, a natural warming of the equatorial Pacific that alters weather patterns and spikes temperatures across the globe.
The current El Nino - which formed last month and is too young to have affected this heat wave much - is expected to rank as among the most intense since the weather service began tracking the phenomena in 1950, experts said.
By autumn it has an 81 per cent chance of becoming "very strong" - the top category - according to the US National Oceanic and Atmospheric Administration.