There’s more evidence linking infections during pregnancy with a child’s risk of autism.

The new report, out Tuesday, shows that women who had infections while pregnant were more likely to have children with autism.

The more fevers they had, the higher the risk — and the second trimester of pregnancy seemed to be an especially important time. Women who had fevers in the second trimester of pregnancy were 40 percent more likely to have a child with autism.

Related: Brain Study Suggests Autism Starts Before Birth

The findings, published in the journal Molecular Psychiatry, support the theory that it might be the body’s response to an infection rather than a bacteria or virus that’s damaging the developing baby’s brain.

“Risks increased markedly and dose dependently with fever frequency, with particularly strong effects after 12 weeks’ gestation,” Dr. Mady Hornig of Columbia University and colleagues wrote in their report.

Women who took acetaminophen to lower their fevers were less likely to have a child later diagnosed with autism, although it’s too early to say whether the acetaminophen — the active ingredient in Tylenol — lowered the risk. None of the women who took ibuprofen had children with autism but so few women took ibuprofen that it’s hard to say what the effect was, the researchers noted.

“This study, using a large, well-characterized sample, confirms the association between fever and risk for autism spectrum disorder,” said Thomas Frazier, chief science officer for Autism Speaks, who was not involved in the study.

“The research also clarifies that the relationship is strongest in the second trimester. Interestingly, the strength of the relationship increases substantially with three or more maternal fevers, and anti-fever medications like acetaminophen may reduce the risk of autism.”

Related: More Studies Show Vaccines Do Not Cause Autism

Columbia’s Dr. Ian Lipkin believes it may be the fever or some other aspect of the body’s inflammatory response to an infection that may be damaging the brain of the fetus. Lipkin, who took part in the study, also worked on research published earlier this year linking herpes infections with autism.

Viruses can infect and damage a developing baby's brain — Zika is the most notorious now, but rubella and cytomegalovirus can also cause severe birth defects.

“The research also clarifies that the relationship is strongest in the second trimester."

Lipkin believes that with autism, however, it's the mother's immune response that's causing the damage. It may be that inflammatory chemicals such as cytokines are crossing the placenta and affecting the developing brain of the fetus, he said.

Surveys by the Centers for Disease Control and Prevention find that as many as than 2 percent of U.S. kids have been diagnosed with autism — anywhere between 1 in 68 and 1 in 45 children.

The autism spectrum refers to a broad range of symptoms, from the relatively mild social awkwardness of Asperger's syndrome to profound mental retardation, debilitating repetitive behaviors and an inability to communicate.

There's no cure and no good treatment.

There are genetic links. If one twin has autism, the other twin is very likely to. There's also growing evidence that infections in pregnancy might play a role.

A 2013 study found that women who had the flu while they were pregnant were twice as likely to have a child later diagnosed with autism. Those who had a fever lasting a week or longer — perhaps caused by flu or maybe by something else — were three times as likely to have an autistic child.

Related: Flu, Fever in Pregnancy Linked With Autism

In the study discussed Tuesday, the Columbia team used a survey of 95,000 children born in Norway. The mothers were followed in real time during their pregnancies and all infection and fevers were documented. Then the children were followed up to see which ones developed autism.

“Maternal exposure to second-trimester fever was associated with increased autism spectrum disorder risk,” the team wrote.

That doesn’t mean women should panic if they get a fever during pregnancy. It’s common for women to have some sort of fever while pregnant — at least 20 percent of pregnant women in the U.S. have fevers at some point.