Answer in Details
On Somvati Amavasya, which is the new moon day falling on a Monday (a day especially sacred to Lord Shiva), devotees perform special rituals and abhishekam (ritual bathing) of the Shiva Lingam with water, milk, and sometimes black sesame seeds. The use of black sesame is said to please Lord Shiva, as it symbolizes purity, the removal of negative energies, and the merit of ancestors.
It is also a common practice to offer black sesame during prayers for ancestors (Pitru Tarpan) on Amavasya, as Lord Shiva is regarded as the lord of time and death (Mahakaal), and worshipping him with these offerings is believed to bring peace to departed souls.
In summary:
Yes, offering black sesame at a Shiva temple on Somvati Amavasya is an auspicious and recommended practice according to Lord Shiva’s teachings and tradition.