The mean and unpredictable winter of 1985 eased its grip on the Washington area yesterday, but much of the eastern half of the nation continued to suffer relentless cold with 117 weather-related deaths from Michigan to Mississippi and a state of emergency declared in Florida to help save its citrus crops.

Weather forecasters predicted moderating temperatures here for the next several days, but the toll in suffering already has been considerable.

A woman and her two sons died early yesterday in a house fire in rural Charles County in Southern Maryland that fire officials blamed on an overworked furnace. The District of Columbia medical examiner's office confirmed that a 61-year-old man died Monday of exposure in an abandoned house in Southeast. And several persons were routed by a fire, started by an electric space heater, that gutted a three-story house in far Northeast. One person was slightly injured, according to D.C. fire officials.

After two consecutive days of record-breaking subzero temperatures, the official thermometer at Washington National Airport yesterday crept up to a relatively balmy 32 degrees at 4 p.m. Even so, early-morning temperatures as low as 10 degrees stalled cars, burst water pipes and closed 19 schools in the area for lack of heat. Other schools started late.

All area schools were expected to open at normal times today.

In Frederick County in Western Maryland, all 44 public schools remained closed "because the school buses wouldn't start," said a county spokeswoman.

Closer to Washington, there were a few tentative signs that things are returning to normal. Utilities reported demand for electricity was down from record peaks on Monday. There were no cold-related breakdowns of Metro subway trains, and the heaters on city buses were working "tolerably well," according to Metro spokeswoman Marilyn Dicus.

In addition, the National Weather Service outlook for the next several days calls for near-normal temperatures -- 20s at night, 30s to 40s during the day -- and little precipitation, except possible snow in the mountains of Virginia and Maryland on Friday and Saturday.

"Sounds good to me compared to what we've had," said forecaster Walter Green.

But the warming trend also has uncovered problems hidden by the cold. Many water pipes concealed in the walls of area homes burst during the cold earlier this week but did not become evident until yesterday when the ice in the pipes began to melt, flooding basements, bathrooms and kitchens. Area plumbers reported being besieged by a new round of emergency calls.

At the Interior Department downtown, a burst water main on the seventh floor sent water spilling down elevator shafts, a department spokesman said, and scores of employes were sent home early.

Elsewhere in the country, Florida Gov. Bob Graham declared a state of emergency yesterday after two nights of record low temperatures that damaged citrus, sugar cane and vegetable crops throughout much of the state.

Under provisions of the emergency, Graham modified weight restrictions on trucks carrying produce so that growers can get their crops to processing centers as quickly as possible. He said his office will provide "whatever assistance we can."

Many Florida cities reported freezing temperatures yesterday morning. It was 10 degrees in Tallahassee and 28 degrees as far south as Hollywood. St. Petersburg and Sarasota reported light snow. It was 34 degrees at Miami Beach, and Key West, 90 miles from Cuba, reported a chilly 49 degrees.

To the north, new snow blanketed the country from Michigan to Vermont and as far south as Kentucky and North Carolina.

Three-foot drifts of snow blocked roads in Buffalo, and New York Gov. Mario Cuomo declared a state of emergency in five surrounding counties. A 134-mile section of the New York State Thruway was closed Monday, and 66 miles of that section remained closed yesterday.

Warnings of gale-force winds were issued for such widespread points as the Great Lakes, the coast of New England and coastal South Carolina.

In the Charles County fire near rural Nanjemoy, Sherline Owens, 28, and two of her children, Paul, 9, and Carl, 5, were found dead by firefighters. According to Maryland state fire investigators, the family had turned the house furnace off Monday when it when it malfunctioned but turned it back on to fight the cold yesterday. Fire erupted in the wood frame house about 4 a.m., firefighters said, and was brought under control an hour later.