Although last week's successful implant here of the first permanent artificial heart is likely to prompt "tremendous demand," officials at the University of Utah say they will proceed cautiously before additional attempts at the "highly experimental" procedure are made.

Dr. Ross Woolley said today that another permanent artificial heart will not be implanted in another patient with inoperable heart disease until the case of Barney B. Clark, the first recipient of the plastic-and-metal device, is reviewed by the university and sent to the federal Food and Drug Administration for approval.

"We want to forestall a rush to the gates," he said, but added that there was little doubt that approval for a second operation will be forthcoming in weeks or months "given the apparent success of this operation." The university already has permission to do seven implants in people undergoing regular heart surgery who are not expected to survive the operation, but such candidates have been difficult to find, added Woolley, who is in charge of the artificial heart subcommittee of the panel that must approve all human experimentation here.

His remarks came as Clark, whose plastic-and-metal heart has been beating steadily in the more than three days since it was implanted, was enjoying a Sabbath day of rest following minor surgery Saturday night that successfully corrected an air leak out of his lungs and into his chest wall.

Chase Peterson, university vice president for health sciences, reported that Clark continued to recover "very well" and remained in "serious but stable" condition. He was sipping juice, his vital signs were normal, the air leak had stopped and swelling in his chest and neck had gone down, he said.

He characterized the "minor complication" as a "pause, not a delay" in Clark's steady recovery. But emotionally, the mood today was "more somber" in the guarded intensive care unit after Saturday night's surgery.

Peterson said the medical team's goals are to strengthen Clark until he has a "general feeling of robustness," avoid further complications, have him take more food by mouth, and have him stand "today or tomorrow."

At one point today, according to one of his surgeons, Dr. Lyle Joyce, Clark sat up in bed and with some effort swung his legs for five minutes.

While Clark's day-by-day progress continues to capture worldwide attention, interest in the new procedure is already turning to long-range issues.

While the procedure will remain "highly experimental" in the near future, Woolley said it was not too soon for society to begin addressing "thorny" economic and ethical issues that could come with widespread use of the plastic-and-metal heart. These include:

Who will pay for the expensive new procedure?

Should it be limited, and, if so, who should benefit?

What will be the quality of life of the recipients, attached to an external power source for the rest of their lives?

Should the recipients have the right to disconnect themselves from their machinery and die?

"We need to avoid some of the problems we've had in the past with new technology," warned Woolley. "We need to be very cautious" about "indiscriminate use."

He cited the example of kidney dialysis, a procedure initially rationed to a select few patients whose numbers grew dramatically when the government agreed to begin paying for it. Now running up a tab of more than $2 billion a year, kidney dialysis is "perhaps too widely used," said Woolley.

In comparison, heart transplants, which have had checkered success since they were begun in the late 1960s, are still sharply limited, in part because of the shortage of organ donations and the individual cost, more than $50,000. He noted that at the most successful center, Stanford University, the patient must bear the financial responsibility.

Dr. David Banta, assistant director of the congressional Office of Technology Assessment, voiced concern that the artificial heart may start out as an option for "the rich" which will put pressure for more widespread use. "We're already foregoing a lot of opportunities," he said, given Reagan administration cuts and the cost-conscious climate which is reducing basic health programs.

Despite the inevitable debate and controversy, developers of the artificial heart say it would be "disastrous" to set limits until more is learned about the machine's success.

Dr. Robert Jarvik, who designed the artificial heart, and Dr. Willem Kolff, a pioneering scientist who heads the artificial organs program here, estimate that demand for the heart may fall in the range of 50,000 people annually. At the moment the machinery costs about $20,000 and hospitalization and surgery are estimated at more than $15,000, but costs could well exceed $50,000.

Jarvik and Kolff head a small company, Kolff Medical, that intends to move the artificial heart from experimental to commercial use, should the initial operations prove successful. They envision more routine use beginning within five years and argue that the man-made heart could prove cost-effective, depending on the number of years it can prolong a person's life.

While the artificial heart used by Clark is attached by tubes to a cumbersome external power source on a large cart that severely limits mobility, Jarvik is confident that a more portable power pack the size of a camera case will be ready for human testing within the next few years.

His company is donating the equipment for the first two artificial heart implants, but the financial arrangements after that have not been resolved. Kolff said that a private foundation has donated $50,000 to help defray costs for the early procedures and university officials also plan to explore the possibility of private insurance reimbursement.

In Clark's case, both equipment and doctors' time are donated.

Kolff, inventor of the kidney dialysis machine, believes that the only limits on future use of the artificial heart should be "that the patient has a reasonable chance to a reasonable existence."

This quality-of-life question is central to the device's acceptibility to future patients. The concern is what long-term reaction a recipient will have to living permanently with a mechanical heart.

Kolff has said that a patient should have a right to terminate his life, and has suggested that a key used to turn the machine on and off and to switch to backup systems could be used to this purpose.

Peterson said all of these future-oriented questions were "honorable to be raised," but he cautioned that concern about the applications should not stand in the way of the research. Otherwise, he said, it would be like "telling Galileo, don't look at the heavens because you may see something that will give us a problem that doesn't yet have an answer."