© ReutersFlood warning: The National Weather service said a year's snowfall in Buffalo, NY, could melt by Thursday
The heat wave is expected as an intense cyclone sweeps north east from the Midwest, driving warmer climes into West Virginia, Maryland, New Jersey and New York.
It could spell a moment of relief for Minneapolis after an historic stretch of freezing temperatures that has lasted 12 days - the longest since 1880.
Emergency services are still shoveling snow to clear the area and rescue civilians.
At least 13 have been killed by the extreme weather.
The NWS predicted temperatures would start to climb above freezing by early Sunday, reaching 60F by Monday.
Temperatures in western New York will stay above freezing until at least Tuesday night, with highs of nearly 50F on Sunday and nearly 60F on Monday, the Weather Service said.
"The warming will bring melting. The melting will bring water. Water will bring floods," New York Governor Andrew Cuomo said at a news conference.
"We are preparing now for more flooding than we have seen in a long, long time," he said. "We've never had this much snow and this much melting of this much snow in a short period of time."
Some areas should expect five to six feet of water, Erie County Executive Mark Poloncarz said.
To prepare, area residents said they were moving valuables out of their basements.
Sections of the New York State Thruway will reopen on Friday afternoon to move vehicles and help remove snow, Cuomo said. Some 140 miles of the thruway had been closed.
Experts warn the exact figures are still vague and they are taking samples of the snow to gauge how likely the flood risk is.
Initial research found rising dew points and winds pointing south will 'make for a more efficient melting of the snowpack'.
At least it is melting this time around. What about the next?