Most children admitted to intensive care with a serious inflammatory complication after getting Covid-19 didn’t have serious lingering issues a year later, according to a study of data collected from hospitals across the U.K.

As the highly contagious Delta variant sweeps across the world, doctors say they are worried about its effect on children, especially those who are unvaccinated. In some parts of the U.S., more children have been hospitalized for Covid-19 treatment recently than at any time during the pandemic since U.S. authorities began tracking the data last year.

The U.K. study tracked the health of children with multisystem inflammatory syndrome, or MIS-C, a rare condition that can occur in children several weeks after Covid-19 infection. It can involve many different organ systems and lead to issues with the heart, including aneurysms in the coronary arteries, arrhythmias and problems with heart function.

Without the proper diagnosis and management, which often involves the use of intravenous immune globulin or corticosteroids, MIS-C can lead to organ damage or even death. More than 4,400 cases of MIS-C were reported among children in the U.S. during the pandemic as of the end of July, according to the Centers for Disease Control and Prevention.

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Most children seemed to recover from MIS-C without any serious long-term problems, according to researchers in the U.K. who collected data on 68 patients under the age of 18 admitted to intensive-care units with MIS-C before May 10, 2020.

The study tracked follow-up visits up to April of this year. None of the children died, they said, and only two patients were readmitted to a hospital’s intensive-care unit at some point. The researchers said the readmissions weren’t related to MIS-C. And although 19 patients with MIS-C had coronary aneurysms when they arrived at the hospital, 14 were back to normal one year later. A coronary aneurysm, or a bulge in one of the blood vessels that feeds the heart, can result in rupture, bleeding and possibly death.

Ten of the patients with MIS-C had coronary arteries that looked abnormal when they were first admitted, and nine of those cases looked normal a year later, the researchers said. Thirty-nine patients had signs of weakened heart muscle upon admission. All of those cases were resolved a year later, they said.

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The study looked at the sickest children with MIS-C, said Patrick Davies, a pediatric intensive-care physician at Nottingham Children’s Hospital and lead author of the study.

“It’s a good sign that the sickest patients had such a high rate of full recovery,” he said. “There’s a certain amount of reassurance here.”

He and his colleagues noted in a research letter published Monday in JAMA Pediatrics that their study was limited by the relatively small number of children and a lack of consistent follow-up protocol.

The study’s results are good news, but more research needs to be done to confirm its findings, said Mobeen Rathore, chief of infectious diseases at Wolfson Children’s Hospital in Jacksonville, Fla., who wasn’t involved in the study. He said he was relieved to see most patients who had heart-vessel issues recovered from them.

“There’s a subgroup where MIS-C affects the coronary arteries. As pediatricians, we’re really worried about that,” he said.

Wolfson is bracing for an uptick in MIS-C cases as more children fall sick after contracting the Delta variant. Dr. Rathore and his colleagues are making sure medical staff know exactly how to recognize MIS-C and know best practices for management, he said.

“We have to be prepared,” he said.

Write to Sarah Toy at sarah.toy@wsj.com