That top-loading automatic in your laundry room cost you, beyond purchase price, around $84 every year if you wash at the national average rate of eight loads a week.

The washing machine, which is a part of nine out of 10 American households, uses up a little less than one per cent of the national energy expenditure. That's enough to get the federal government into the act.

Washington is saying this: hot is cleaner, but cold is cheaper. Ninety per cent of the energy used in washing machines is the hot water, so that's the logical place to cut down.

The Federal Energy Administration is advocating two ways to make laundering colder, and thus more energy-efficient: rinse in cold water, and cut the overall temperature down.

The FEA, in accordance with the 1975 Energy Policy and Conservation Act, has established energy efficiency improvement standards for 10 major home appliances. Washing machines, they say, should be improved 47 per cent by 1980.

Yesterday the FEA began hearings to determine what manufacturers think about the proposed standards. Apparently it isn't much. Most washing machine manufacturers said they couldn't meet the standards by 1980.

The reason? Consumer acceptance.

"I read an awful lot of letters from our customers," said Kishin J. Gursahaney of White-Westinghouse Appliance Co. "There are people who honestly believe with their whole heart that you can't properly do a load of laundry without some hot water."

Those people needn't worry. The FEA is asking not that we sacrifice our hot water for the entire load, but only for that final rinse.

The rinse, according to a home economist at Procter and Gamble, uses up almost half the 50-gallon wash.

"I think the industry is moving toward cold-water rinsing, and that is a decision with which we would concur," said the Procter and Gamble economist.

"When it comes to washing, though," she added, "that's a different story. Cleaning is harder as temperature gets lower-fatty components of the soil harden and chemical reactions don't occur so easily."

But the FEA is asking for colder laundry, within reason.

"There are some cases we'd never deny," said an FEA official. "Things like baby clothes should be washed in warm or hot water."

He said that later this year a broadcast campaign will advise Americans to wash their clothes at lower temperatures. The ads will be "slightly anthropomorphic," he said, not denying the possibility that we will be seeing talking washing machines on the television screen.

If this furor over laundry temperatures comes as no shock, that's because the American public has been, of its own accord, cooling down the wash for several years.

The Procter and Gamble official said that in 1970 half of all laundry loads were washed in hot water, 35 per cent in warm, and 15 per cent in cold.

By 1976, however, hot and warm had reversed. Half of all loads were washed in warm water last year.

She attributed the change to an increase in permanent-press clothes, which can be washed at cooler temperatures, and an upsurge in bright colors that fade in hot water.

"And of course," she added, "utility bills have gone up, and that has to be part of consumer behavior."

FEA supervisory engineer William Walsh estimates that if the 47 per cent improvement target is met the annual household expense of $84 will be reduced to about $57.

But there's a tradeoff in this federal energy-saving tip: the savings of rinsing cold are offset in part by extra energy needed to dry the clothes.