THE WHITE HOUSE could be heating its water with the sun by the end of the year. President Carter, who began his term by commissioning a solar-heated inaugural stand and has gone on to call for a major energy effort from the American people, is putting his own house in order. He has asked the Energy Research and Development Administration to study all ways to use solar energy at the White House.

The ERDA feasibility study for a solar-energized White House has been under way for not quite a month, it was learned. The study is expected to be completed within another 30 days.

While looking to the sky, the White House is going ahead, as are many homeowners, with the more conservative project of adding insulation in the roof. A second study on other energy-saving techniques for the White House is being conducted by the General Services Administration.

Both projects are being coordinated with Rex Scouten, the chief usher of the White House, who actually is the building's manager. Scouten said he is "convinced we will have a solar energy system soon at the White House."

"Solar energy for the White House is technically feasible, economically promising and architecturally possible," said Ronald Scott, assistant director of solar heating and cooling for ERDA, who is directing the feasibility study.

"Of course we can't have any visual pollution from the collectors. The solar energy will have to be competitive with fossil fuel. And it has to perform properly. But there aren't any real problems with any of these.

"Heating the White House's water with solar energy is certainly the easiest to do and the most cost effective. Air conditioning with solar energy will be the most difficult part of the plan, but we're considering that as well."

The White House has a great deal going for it as a candidate for solar energy, Scott pointed out. "It's a great thermal sink (a natural heat collector and storer). That massive stone construction is just wonderful. And if you had it to rebuild, yoy wouldn't orient it any differently at all."

The White House lines up on an eastwest axis with the long walls facing south and north, a major recommendation for collecting what is called "passive" (non-mechanical) solar energy. All of the public rooms have major windows on the south, and the three smaller drawing rooms - the Red, Green and Blue Rooms - have only south windows. South windows get significantly more energy from the sun than do other windows.

(For some purposes, they get too much. Several years ago, the White House installed Solarex, a thin, colorless plastic film on the east, west and south windows throughout the house to cut down on the ultra-violet ray destruction of the fabrics.)

The White House also has a fair amount of flat roof space on which to mount solar collectors, according to Scouten. "Though they'll have to leave us room to get to the flagpole to run up the flag," he said.

With present technology, it probably wouldn't be possible for the White House to get all its energy from the sun. Current recommendations call for half as many square feet of solar collectors as there are square feet of house, which in the case of the White House's 375-odd rooms would mean a lot of collectors. The hot water consumption is said to be about 550 gallons a day, well within the capacity of collectors. The usual recommendation today is a solar collector for each member of the family.

So far, no one has made any firm estimates as to what all of this will cost. A family of six or seven people would need about six solar collectors. A kit with six collectors and a heavily insulated hot water tank costs about 2,5000 installed by Intertechnology/Solar Corp. of Warrenton, one of the larger area solar energy companies. Norris Beard, Intertechnology's marketing manager, says such a system, replacing an electric hot water system, could be expected to pay for itself in about six years.

Intertechnology had suggested a solar system to heat the White House outdoor swimming pool when when Gerald Ford first had the pool dug, but for some reason that no one has yet explained the project didn't go forward. Ford used an electric heater and swam nearly every day. The Carters, according to Scouten, don't heat the pool electrically at all and only swim in good weather. "We use a device called a 'Solar Blanket,' a kind of pool cover that looks very much like that bubble packing material," Scouten said, "and that does collect and keep a certain amount of heat."

In the meantime, the White House top floor is being reinsulated, replacing the cork-like solid material put in during the 1952 remodeling with an Owens-Corning Fiberglas 703 semi-rig board with a foil reinforced craftpaper cover, Scouten said. "We started in January, and we've been doing a bit at a time as we can when the family is out of town. All that hammering makes a lot of noise."

There isn't any way, short of building new walls inside or out, to put insulation in the walls, the chief usher said. "The side walls are sandstone on the outside with lath laid directly on it and plaster over that for half an inch."

Storm windows or insulated glass windows for the White House haven't yet been considered feasible, Scouten said. "The glass is handblowen. It must date way before the 1930s, perhaps as early as 1900. It's like that made in the 1850s. It's really beautiful."

The Octagon, the nearby historic home of the American Institute of Architects, has plexiglass shields screwed into its window frames for insulation and burglar proofing. Scouten didn't think that would be feasible for the White House. "We have to wash windows every day."

Besides keeping the White House at 68 during the winter, the staff is careful not to cool it below 78 in summer. "We don't run the air conditioning to cool it at all," Scouten says, "just to keep the humidity below 60 per cent. Anything else would damage the several million dollars of furniture and objets d'art."

So far, the White House hasn't seriously considered going back to three energy-saving devices it once had& awmings, greehouses and sheep.

The Friends of the Earth mid-May newsletter, in the Sunspots column by Helene Kassler, suggested a return to those methods, along an ambitious "housewarming" plan commissioned by Kassler from Richard Fernau of Dumbparts, a solar energy system designer. (Fernau consulted the Berkeley Solar Group solar system design and consulting firm and Bruce Corson of the California Office of the State Architect.) The solar experts calculated that the WHite House could save half of its $61,000 November to February steam heat bill with these measures:

A greenhouse at the south entry and two semicircular greenhouses stretching along almost the entire south side. An internal colonnade of water-filled steel columns would absorb and store solar heat.The water columns would provide a heat source for a heat pump. The greenhouse walls would be insulated with styrofoam peanuts.

Skylights in the corridors for light and heat.

Collector panels for solar water heating.

Sleeping porches with movable lattice screens with oval cutouts to enjoy the view.

Red, white and blue canvas awning sor south-facing windows and the greenhouse roofs.

Sheep to trim the lawn and provide natural fertilizer, saving, according to Kassler, 350 gallons of gasline at least per year.

A vegetable garden fueled with compost.

All of these measures, except for the solar collectors, have historic precedents. Awnings were used on the south side up until at least the President Harry Truman remodeling. President Taft's wife insisted upon keeping a cow grazing on the White House lawn. President Wilson used sheep to keep the lawn trimmed. Scouten, while quite enthusiastic about everything else, is not so enthusiastic about the sheep. "I worry about people watching where they step. And think of the sheep when they fire off 21 gun salutes."

A great crystal palace of greenhouses topped with glass cupolas plus glass cupolas atop twin White House East and West Wings were suggested by architect Fred D. Owen in a plan commissioned by Mrs. Benjamin Harrison, who wanted to remove the President's office from the White House proper. The grandiose scheme was not built.

The White House had extensive greenhouses from at least 1857, and by 1900 there were greenhouses both west and south of the house. It was President Theodore Roosevelt who yelled "smash the greenhouses," and it was done to put up the West Wing. Jefferson had in 1807 ordered low-lying east and west pavilions. Jefferson, in his anonyomous entry for the competition to design the White House, suggested a plan with a skylighted dome, and he fought Benjamin Latrobe hard to put in a sky-lighted Capitol dome. Jefferson was also responsible for the White House earth berms and tree planting. Deciduous trees are well known as give cooling shade in summer while allowing winter sun to come in.

One of the early suggestions to put solar heat in the White House came from Ken Bossong, who edits People and Energy, a newsletter of the Center for Science in the Public Interest. Bossong sent a letter to Carter on Jan. 30 advocating solar energy for the White House "to dramatize both the need and potential for solar energy utilization . . . Our studies and those of ERDA indicate that solar water heating is cost-effective in Washington, D.C., and practically all parts of the United States . . . Moreover a national program spearheaded by the White House to convert to solar water heating could utimately reduce the U.S.'s energy consumption by 4 per cent . . . A White House solar unit could be most effectively exploited if used as the launching of a major federal solar buildings program."

The letter was co-signed by Alan Okagaki of the Center plus Harriet Barlow of Rural America; Craig Decker of New England Technology Network; and David Morris, Institute for Local Self Reliance. Bossong later made the same suggestion in a Letters to the Editor column of The Washington Post.

Replying to the Bossong letter, Robert I. Hanfling, acting assistant administrator, Federal Energy Administration, Energy Resource Development, wrote in a letter received May 9: "President Carter has asked me to respond to your letter of Jan. 30 . . . We have been advised that an appropriate federal agency will be asked to initiate a feasibility study to determine the technical, architectural and economic feasibility of installing solar in the White House as you have suggested."

Kassler initiated her study after hearing about Bossong's letter. Later she forwarded the Friends of the Earth plan to Charles Warren, chairman of the Council hopes he'd show it to President Carter. He hasn't. "I haven't really thought about it," he said the other day, two days after he had received it. "I haven't decided who or if I should show it to at the White House. My office hasn't made any recommendations for putting solar collectors on the White House at all. But we have suggested recycling paper."

On the other hand, ERDA's Ronald Scott is quite enthusiastic about solarizing the WHite House. "I believe in it.It could have a nationwide impact for energy saving. I think it's marvelous we have a leader who thinks these ideas are worth investigating."

ERDA's plan would have to be approved by the National Park Service, which "owns" the White House, and then would have to be executed by GSA, all under the watchful eye of Rex Scouten (who under the previous President, had to put in a swimming pool and under the one before that had to cover up a swimming pool).

Jimmy Carter has one disadvantage over Harry Homeowner in the installation of solar heat and conservation measures. Even if the expected tax deduction for such measures goes through Congress (what the Friends of the Earth call "Cartervation"), he still won't be able to deduct if from his income taxes. His rent is free, and utilities are provided.

No one so far has suggested a windmill for the White House. But some say windpower would work well for the Congress.