The federal government's war on excessive air condition - to be fought with $7 million enforcement effort and a nationwide "hot line" for turning in violators -- will formally take effect Monday.

After that day, according to an order President Carter signed yesterday, it will be illegal for owners or managers of most nonresidential buildings to set thermostats lower than 78 degrees.

The order, which will be in effect through April 16, 1980, also prohibits heating of nonresidential buildings above 65 degrees in the winter. It also limits hot water temperatures -- except where health considerations require higher levels -- to a peak of 105 degrees, about 40 degrees lower than the level provided by most domestic water heaters.

All of this could save the nation between 200,000 and 400,000 barrels of oil per day, according to the Department of Energy -- about 2 percent of total U.S. consumption, but about 10 percent of the amount normally used for heating and cooling.

Congres gave the president standby authority to impose temperature controls in May, and the Energy Department issued final regulations for the effort last week. Carter offically triggered the program yesterday with a declaration, required by law before the controls can take effect, that the United States is experiencing a "severe energy supply disruption" warranting the restrictions.

John Millhone, the Energy Department official running the new program, said the implementation date was delayed until Monday to give building owners time to find out about it.

The controls will apply to just about every building, large or small, where people work, play, study, shop, worship or dine out. Homes and apartment buildings are excluded, as are hospitals elementary schools and guest rooms in hotels.

Restaurants and food processing firms will be excluded from the hot water temperature limits because health codes generally require temperatures of at least 160 degrees for dishwashing and other hygienic operations.

Other specific exemptions will be provided for buildings with unusually complex heating and cooling plants. Indoor swimming pools will be exempted from the 65-degree wintertime standard, on grounds that swimmers might otherwise risk illness.

Violators will theoretically be liable for fines up to $10,000 per day, but Millhone said yesterday that negotiated settlements will be the preferred enforcement tool.

Millhone emphasized, though, that "we want this program to be taken seriously." To see that it is, the federal government will distribute $7 million to state and local governments, which will bear the brunt of the enforcement burden.

As the Energy Department sees it, the states will probably assign enforcement to building and health inspectors who already make regular inspection tours of most buildings.

In addition, the government will encourage public informant efforts by establishing a national hot line that people can call toll-free to tip off enforcers to buildings that are illegially cool or warm.

The hot line number -- which will be different from the number set up for reporting violators of gasoline price control rules -- will be made public later this week..

The regulations do not require building owners to post a thermometer in a public place so that people can judge compliance. Anyone who wants to help enforce the rules, Millhone said, "can buy a thermometer for about a dollar."