The puppy died in a terrible way. Sandra Alexander had left a big pot of scalding water on the bathroom floor, ready to use for her children's bath. While she was out of the room, they had put the puppy in the tub and poured the water on it.

"I thought, 'What if it had been one of my kids?'" Alexander said. That was seven years ago. Every winter since then, she said, the big pots of scalding water have been part of life because the public housing project where she and her nine children live never has provided adequate hot water or heat.

Each winter, many low-income people in Washington are cold - chronicallY, indisputably, shiveringly cold. While most people can manage to be warm and cozy when the snow falls, and while many people can afford to add expensive storm windows and insulation to their homes, these low-income people cannot.

They survive by opening their gas ovens and running them all the time. They wear heavy clothes indoors. It is a miserable, subhuman way to live.

It is difficult to know how many people suffer this way, but the city's housing department recently sent letters to landlords of more than 300 buildings where there were complaints about lack o heat last winter. The letters warn the landlords not be let it happen again.

Of course it will.

Asked about the problem by a reporter, city officials often seemed to shrink within bureaucratic shells making carefully guarded statements or asking not to be identified by name.

They are familiar with the problem. "Last winter there were a lot of cases of no heat," said a woman at the city's office of Emergency Preparedness. "Landlords hadn't paid bills, buildings ran out of oil or there were mechanical problems. We take their problems and try to sheer them through the system, the bureaucracy and red tape, so that citizens can get the aid that they're in need of."

All this is small comfort for Alexander and her children. As inhabitants of public housing, they have the city as their landlord. The very city housing department that sends warning letters to landlords has itself let them suffer through seven long, cold winters without adequate heat or hot water.

"Let tell you it's hell, it's just hell," said Alexander, a large woman who frames her sentences solidly, with conviction. "You can't do anything when you're so cold. You sit in one place and you try to get warm and you can't. People are in their houses walking around with coals and jackets on. And kids - everybody gets into one bed, they pile all the blankets and coats on . . ."

On school days her 11-year-old dauther. Ayesha, gets up at 3 a.m. to take a bath because there is a little hot water in the pipes then. At 6, the rest of the family is up, and Alexander is boiling water in her big pan on the gas stove. The water is carried to the bathtub on the first floor.

It takes seven trips upstairs from the basement kitchen to carry enough of the scalding water for everyone to have a bath. Each trip is a grim invitation to disaster.

The gas oven is left on and open most of the time to provide what heat the house has - another invitation, this time to asphyxiation, should the flame go out while everyone is asleep, or to death by burning.

When it gets very cold, Alexander supplements the oven heat by turning on the range burners full blast.

Sometimes it seems the children have colds that last all winter, that they never get well until the warm weather comes again. When the doctor chastizes Alexander for not taking proper care of them, she tries to explain why she cannot.

Her life has not always been like this. She was raised in Washington by grandparents who lived comfortably.

"I led a sheltered life. I always had clean clothes, heat and hot water. My condition of being poor was imposed on me. I'm divorced, and I have the kids to raise. I expect a decent place to live in," Alexander said.

Her projects is called East Capitol Dwellings - a dreary, sprawling, 577-unit collection of brick apartment buildings and townhouses far out East CAPITOL Street near the District line.

Some of the buildings are boarded. At night, when scores of teen-agers gather on a nearby corner, an air of danger is present windows frequently are broken, and Alexander said she must pay the management S7 a window for repairs.

The management is the city government, backed financially by the federal government. Alexander pays only $75 a month in rent for her spacious townhouse, but on her budget this is a tight squeeze. She receives welfare payments each month.

The $75 includes hot water and radiator heating, both supplied through a pipe distribution system from centrally located boilers. Alexander pays the gas and electric bills, so keeping the oven on all winter costs money that she should not have to pay under terms of her lease.

"I moved in in 1971 or 1972 she recalled. "I wanted to get a bath, and the water was cold. So I asked a neighbor, and she said. 'Well, we don't have hot water out here.' I thought she meant just for that day. But I called around and found out it was common knowledge that there was never hot water . . ."

Alexander and other tenants have complained over the years with little success. Many were afraid to complain for fear of being evicted. Despite the heat problems, Alexander has not moved because she does not know where things might be better.

The experience has taught her something about the government and government officials.

"It's their attitude. They may as well come out and say it (that they don't care." She said a former manager told her. 'You think I'm going against the government for you? They pay me my salary.' He said, 'If you think you can do anything try it.'"

Alexander does not understand why years go by and the government does nothing. She is deeply disturbed.

This is the government itself? At first (the former manager) did get kinda concerned because I was complaining everywhere. He said they needed new boilers and didn't have the money, which I didn't believe. To me, the government can find money for anything they want. They have missiles, they have research, but they couldn't find the money to put the boilers in so we could be warm," she said.

Finally, $551,766 has been found, and boilers are being installed under the supervision of a D.C. Superior Court judge. Last April, with help from Neighborhood Legal Services attorney Lynn E. Cunningham, the tenants sued the city to demand action.

Whether the suit speeded the boiler installation and what stage that installation is in are no clear.

Cunningham wondered. There are a lot of people suffering. Many of the units are not really weatherproof. In lots of the units, water blows in under the living room door so you get puddles when it rains."

City officials say that the basic problem has been solved with installation of three new boilers and that now only the sinks need to be ironed out of the system. Cummingham says people in the project still do not receive adequate heat and hot water.

"Why is the city not producing?"

"We have installed three new boilers, and I'm told we have adequate heat and hot water everplace," said Monteria vey, the city's top administrator for public housing last week. "By the end of December, we should have another boiler for hot water, which should make the hot water even boiler. We propose to put in a new (pipe) distribution system when the weather breaks next spring."

Asked how Alexander could have gone seven years with little or no heat and hot water, Ivey said: "When somebody complains, we go out and see what the problems are. We would not allow anybody to stay in a unit for seven years without heat. There was always some heat and hot water. It may not have been adequate because you're dealing with mechanical equipment . . ."

Alexander conceded that there has been some hot water - usually for that brief period at 3 a.m. - and beat sometimes, but never enough. She noted a radiator in her living room and said it never was any hotter than at that time. It was lukewarm.

"When you talk to Ivey you get an impression that there's nobody there, nobody's at home upstairs," attorney Cunningham said. "He's totally passive. That atmosphere pervades the whole (situation)."

Abraham Nance, the city employe who manages East Capitol Dwellings, said the new boilers will bring quite a vast change . . . I'm just hoping that everything is in before it gets real cold."

Robert Ratcliffe. HUD's deputy director for housing, said, "Money as a reason" it has taken years to get the boilers; replaced. "Of course," he added, "if the appropriate people get in touch with the authorities, then expeditious repairs and inspections should be made." HUD funds this and the city's other public housing projects.

Alexander said that she and other tenants got in touch with the authorities many times over the years but that nothing was done.

Superior Court Judge Fred B. Ugast, who has tried to handle the suit in an informal way despite a large caseload, gave up recently and passed the case along to who might have time for formal hearings and court orders that may be required.

Meanwhile, winter approaches.

"This house has really despressed me." Sandra Alexander said. "Sometimes I hate to even come home. I go away from here as much as I can because the house is no uncomfortable. When I first moved here, I began to fix the house up, but I got disgusted . . . I get sick . . . I can't get myself together to care anymore . . .