CHICAGO (Reuters) - A blistering heat wave finally showed signs of letting up across the U.S. Midwest and Northeast on Sunday, bringing relief to millions after days of oppressive temperatures - just as forecasters warned that a new round of record highs could soon bake Western states.

"It's going to start as soon as tomorrow - really everybody in the Rockies is going to see this heat," said Alan Reppert, senior meteorologist for AccuWeather.com. He said a high-pressure system developing over the Rockies will cause temperatures of over 100 Fahrenheit (37.7 Celsius) in Salt Lake City by Wednesday.

A slow-moving front of cool air from Canada started pushing down temperatures Sunday from Minneapolis and Detroit to Pittsburgh. The temperature in Chicago, which saw three consecutive days of triple-digit temperatures in the past week, was a pleasant 82F (25C) Sunday afternoon, according to the National Weather Service.

New York City and Philadelphia still were hot Sunday, although not as oppressive as in days past, with highs in the lower 90s.

Thunderstorms were expected Sunday afternoon from Maryland on south, with storms in the area for most of the week. The storms also will affect the central and southern Plains states, Reppert said.

The blistering heat wave that scorched much of the eastern two-thirds of the nation with triple-digit temperatures has tied or broken nearly 3,400 maximum and minimum temperature records across the country in July, according to the National Oceanic and Atmospheric Administration.

Dozens of people have died, including a 4-month-old Indiana girl who police say was left in a car outside her home in Greenfield, about 25 miles east of Indianapolis, for an extended period of time when temperatures were above 100F (38C).

Lack of rainfall plus extreme heat is threatening the Midwest's corn crop and leading to wildfires. The latest U.S. Drought Monitor report, released Thursday, showed drought encompassing more of the contiguous United States than at any other time since the report began in January 2000.

"The problem for crops - especially the corn crop - has been the heat and lack of rainfall. It is dry across much of the Midwest and Plains and there is no relief in sight," Reppert said.

The decline in temperatures will be slower in the mid-Atlantic because of the slow speed of the Canadian cold front as it moves south, according to AccuWeather.com.

Power outages continue to plague more than 117,000 customers, primarily in West Virginia, some of whom have not had power for more than a week and may not have their service restored for a few more days.

American Electric Power said it had about 59,600 customers out in West Virginia and about 25,600 out in Ohio. FirstEnergy Corp said it had about 32,200 customers out in West Virginia.