Kara - significes hand. But for Ramayana series Kara is the Rakshas whom Rama killed after Soorpanaga's nose cut. The 3 demons Kara, Dooshana and Trisiras.
The lingam worshipped by Trisiras is in Trisrappalli (trichy)according to Puranas. ( but no literrary or epigrapic proof)
There are 2 places called Karapuram where Kara is supposed to have worshipped. It is also a Thevara Vaippu thalam.
The places called Karapuram are 1. Tirupparkadal Siva temple ( near Kaveripakkam) and 2. Virinjipuram ( also mentioed as Karapuram in epigraphs)
There is also a Karapuranathaswamy temple near Salem.