It happened the first time nine days after his birth, when his mother, Rajeshwari Karnan, says she returned to her hut after leaving him alone momentarily, and found him on fire.
"There was a flame on his belly and his right knee, and my husband rushed with a towel to put it off," Karnan told the New York Times. "I got very scared."
The baby's parents described three similar incidents, even after having been to the local hospital for treatment.
The family traveled to the Kilpauk Medical College Hospital to seek further tests.
In addition to testing for numerous medical conditions, the possibility of child abuse was investigated.
"We are in a dilemma and haven't come to any conclusion," said Dr. Narayan Babu, head of pediatrics at Kilpauk Medical Hospital. "The parents have held that the child burned instantaneously without any provocation. We are carrying out numerous tests. We are not saying it is SHC until all investigations are complete."
Of course, spontaneous human combustion is a highly controversial explanation. The majority of scientists remain unconvinced of the plausibility of the phenomenon.
Local media point out that baby Rahul's home village experienced a series of mysterious fires that burned down several homes in 2004. It was later discovered that phosphorous cow dung used in building materials had a very low ignition point.
Rahul will remain in the hospital for at least a week while doctors attempt to discover the cause of the burns.
Cases where humans have burned down to a pile of ash while their homes and surroundings remain untouched by flames have puzzled experts, but there is no evidence that a human can combust without an external ignition source.
Even the proposed "wick effect" theory, in which a person's body fat can serve as fuel for a slow burn, would require ignition from a lit cigarette or electrical source.
Another proposed theory is that the highly flammable chemical acetone, which is produced and disposed of in the human body, can build up in a person's blood. But tests released this week confirmed Rahul's acetone levels to be normal.