The temple was set on fire late last night and the blaze was doused this morning after villagers detected it, police said.
Superintendent of police Pradip Pujari reached the spot for enquiry.
Nath, who represents the Borkhola assembly constituency in Barak Valley, had created a furore by announcing her marriage with Jacky Jakir without divorcing her first husband.
Nath and Jakir were beaten up and injured by a mob at Karimganj town on June 29.
Meanwhile, Silchar Press Club in an emergency meeting today demanded a probe into the attack on three journalists allegedly by the supporters of the MLA and Jakir at Kalain on June 29.