The government's moral equivalent of war against energy waste heats up today - literally - with the requirement that thermostats in public building be set no lower than 78 degrees.

Under a presidential declaration issued last week, from today through April 1980 it is illegal for most nonresidential buildings to have thermostats set cooler than 78 degrees in the summer and warmer than 65 degrees in the winter.

Building owners and managers who remain cool to the mandate for warmer temperatures have an added incentive to comply - violators of the 78 degree rule are subject to fines of up to $10,000 a day. An energy hotline has been established to encourage the public to turn in cheaters.

Coming in mid-July, the time of peak temperatures for most of the country, the new cooling restriction is bound to affect the comfort - if not the life style - of most Americans spoiled by their air conditioners.

Office buildings, factories, stores, restaurants, theaters, libraries and government buildings are all included in the temperature decree. Since about the only buildings excluded will be homes and apartments, schools, hospitals and hotels, Americans seeking refuge from the summer heat may find themselves confined to their own living rooms.

The higher temperatures are expected to save electricity in about 5 million buildings nationwide, according to Energy Department estimates. Officials anticipate daily saving of up to 400,000 barrels of oil.