(CNN) -- People in a huge swath of the United States were being urged to seek out shelters as needed on Sunday as a historic heat wave continues to bring sizzling temperatures -- including to some who have lost power.
Extreme heat is the leading cause of weather-related deaths in the United States.
Twenty states were either partially or entirely under excessive heat warnings or heat advisories on Sunday, according to the National Weather Service. Temperatures over 100 degrees Fahrenheit were expected in much of the Southeast.
New York City was among the sites in the Northeast facing heat advisories. The National Weather Service said the advisory would be in effect from noon until 7 p.m. ET for the city, with temperatures expected in the mid-90s. When combined with humidity, it could feel like 100 degrees.
Over the past week, nearly 1600 high temperatures have been broken -- including 140 all-time highs, according to the National Climatic Data Center. Statistics for Saturday, when more records were broken, were not yet available.
Meanwhile, a derecho -- or massive storm usually with straight-line wind damage -- that moved across the Ohio Valley to the Northeast on Friday and into Saturday left 13 people dead and millions without electricity. Many remained without power on Sunday.
Some residents in the affected areas, particularly between Chicago and Washington, were likely to see high temperatures in the 90s or even 100 on Sunday, said CNN Meterologist Sarah Dillingham. "Even with areas seeing temperatures in the 80s to low 90s, no air conditioning will still pose a major threat."
"Residents who have no air conditioning are urged to find local cooling shelters or other air conditioned establishments to keep cool. It is imperative people do anything they can to try and beat the heat."
Cities throughout the affected regions offered water at certain sites and opened cooling shelters, including 35 in Virginia alone.
"I'm very concerned with the problems created by the combination of power outages and severe heat," said Ohio Gov. John Kasich, who said it could take up to a week to get the power back up to everybody in the state.
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Kasich also called out the Ohio National Guard to check on and help the state's most vulnerable, primarily the elderly and the ill.
While crews worked around the clock to restore power knocked out by the related storms, hundreds of thousands of customers remained without electricity on Sunday.
As of 3:15 p.m. Sunday, there were still more than 450,000 AEP Ohio customers without power. Similarly high outage numbers were reported by utilities throughout the affected region -- including over 385,000 with Dominion in Virginia, 285,000 with BGE in Maryland (where PEPCO reported an additional 270,000 outages) and upwards of 132,000 with Atlantic City Electric in New Jersey.
The deaths from Friday's storm stretched from Ohio to New Jersey -- most the results of downed trees, as well as the electrocution of one man in Washington.
Virginia had the highest death toll, at seven, with the state Department of Emergency Management reporting an additional fatality via Twitter on Sunday afternoon and noting the deaths were spread across four different counties.
And in New Jersey, 2-year-old and 7-year-old cousins died after a fallen tree crashed on the tent they were huddling inside in Parvin State Park, state Department of Environmental Protection spokesman Larry Ragonese said.
The destruction prompted state of emergency declarations by governors of Maryland, Ohio, West Virginia and Virginia.
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"This is not a one-day situation; it is a multiday challenge," said Virginia Gov. Bob McDonnell, who called it the largest power outage unrelated to a hurricane in the state's history.
In West Virginia, power outages forced the closure of a large number of gas stations after pumps were rendered inoperable.
Brian Duckworth waited in line for gas for nearly two hours in Vienna, along the West-Virginia-Ohio border.
"I wouldn't even be here because I have plenty of gas in my truck," Duckworth told CNN affiliate WTAP. "But I have to get gas for my generators and some backup gas."
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The storm also affected Amtrak service, including shutting down service between Washington and Philadelphia on Saturday.
Those most inconvenienced were aboard a train that ended up grinding to a halt Friday night in Prince, West Virginia, after trees blocked tracks both in front of and behind it, Amtrak spokesman Steve Kulm said.
By late Saturday night, the 232 passengers -- who stayed aboard the Chicago-bound train, which had air conditioning and food -- had been taken off and put on buses so they could reach their final destinations, according to Kulm.
Photos: Storm damage in Washington, D.C.
Emergency rooms in Prince George's County, Maryland, filled up over the weekend by people looking to escape the heat, said Fran Phillips, deputy secretary for the state's Department of Health and Mental Hygiene. She noted that libraries and community centers across the state would stay open late to act as cooling centers.