At least three U.S. drug companies are making a high-stakes effort to develop a drug that would slim down dangerously obese adults by burning off excess weight--thereby inducing a slight fever.

The compounds under study at Lilly Research Laboratories in Indianapolis and, in a less advanced stage, at Burroughs Wellcome Co. in Research Triangle Park, N.C., and Hoffmann-La Roche Inc. in Nutley, N.J., do not attack fatness by the usual route of suppressing the appetite.

Instead, they mimic the metabolic effects of exercise by burning up fat, a principle called thermogenesis.

The FDA estimates that 20 percent of U.S. adults are so overweight that their health is threatened. While the drug is intended for this group, marginally overweight people looking for an easy way to lose weight obviously could also resort to such drugs.

A drug that will burn off fat regardless of diet may be pie in the sky and could produce serious side effects. Diet experts generally agree that the only safe, reliable way to lose weight is to eat less and, for people who can do so safely, to exercise more. The researchers themselves caution that their testing has been confined to animals--rats, mice and beagles.

But the effort the companies are making indicates that they see a large potential market.

"This is really big, really serious stuff . . . , potentially 30 to 40 million dollars a year," said an industry source who asked not to be identified, "and you're not going to take a chance on losing a patent on something like that."

Although it has been known for some time that Lilly was developing such a drug, the company acknowledged it only last November when it published a report on its laboratory tests in Life Sciences magazine. The report described the type of animals used, a rise in body temperature experienced by the obese animals as they lost weight and a weight gain after the treatment stopped. The Eli Lilly Co. has patents pending here and in Europe, which puts it ahead of the other companies.

Any eventual success depends on how apt the animals are as models for humans and on the drug's specific effectiveness on fat cells without side effects or toxicity. One industry source predicted it would be at least five years before the drug would be ready for use in humans--and added, "I'll be the first subject."

A Swedish hospital that has a diabetes expert doing research at the National Institutes of Health in Bethesda has asked to participate in testing Lilly's compound, which is identified only by the code LY79771.

Any human tests in this country would get serious FDA scrutiny for potential side effects, weighing them against the drug's expected benefits.

William Grigg, an FDA spokesman, said he could not speculate on approval for an untested drug, but he noted that many approved drugs have unwanted side effects because "nothing is 200 percent safe."

"If a drug showed great promise, I would think there would be a good possibility of a slight fever being overlooked" for approval, he said.

An industry source said that there was no question that the drugs would have some side effects, but that the developers would be seeking to minimize these so that anything other than fat cells would be affected only by extremely large dosages.

An obese person would take the drug for a week or two without seeing a change, then would lose weight gradually while experiencing a slight fever. When he or she got down to the proper body weight, the drug would cease to have an effect and the supervising doctor would stop treatment.

This phenomenon was borne out in the Lilly report, which said that for some unknown reason animals "on long-term treatment seemed to stop losing weight as they approached lean body weight." The industry source said that fat constitutes 40 to 50 percent of obese people's bodies, compared to normal body fat of about 15 percent.

Dr. Walter N. Shaw, who headed the Lilly project, conceded that an obese person using the drug could lose weight while eating too much and later regain the weight. But, he said, the hope is that people would use the time they are on the drug to restructure their eating habits.

The cost of obesity can be high. Of special concern is the susceptibility of overweight people to maturity-onset diabetes, which tends to occur after age 40. Obese people are also especially vulnerable to cardiovascular disease, osteoarthritis, hernias, gall bladder problems, atherosclerosis, hypertension, kidney disease and cirrhosis of the liver.

The demand for weight-reduction aids is immense. Grigg said that total diet aid sales in 1980 were $311 million, a 50.4 percent increase over the year before. Most of the increase is attributable to a jump from $110 million to $200 million in nonprescription sales.

The FDA estimates that 80 million Americans are overweight and that 95 percent of those who diet regain the weight they lose.

The cost of developing the new drug--including animal and human testing--could amount to between $35 million and $50 million, an industry source said. If one company gets past the development stage and then is beaten into the patent office and the market by a competitor, the slower company's efforts may well be for nought.

"Usually, the first drug in an area like this will get the whole market," the industry source said. "Doctors are creatures of habit."