Nagapattinam Superintendent of Police Durai said the teams have obtained some leads by studying cases of similar thefts in nearby areas in the past.
Fingerprints have also been lifted from the scene of the crime, he said, adding a sniffer dog that was brought in went from the temple to the bus stand.
"We are approaching the investigation from different angles," Durai said.
The theft had come to light on October 10 evening when the priest went to perform pooja and found the lingam, also called 'Suyambu lingam' (created by God), missing and the box in which it was kept was broken.
But renowned archaeologist Dr Kudavayil Balasubramaniam felt the Lingam might belong to the Musukuntha Chola period, one among the early Chola dynasty kings who ruled this area in the pre-sangam era.
He told PTI that Tamil puranas like 'Kanthapuranam' contain references to Musukuntha Chola installing the Maragatha Lingams in seven temples, including at this shrine.