Thiruvaanaikka is one of the five sthalam that fall under the category - pancha bhootha sthalam. This temple is the "Appu sthalam". Appu means water.
It was belived that the Jambukeswarar in the temple was built by Akilandeswari using the water from the kaveri river.
Parvati meditated strongly on Shiva to marry him. Shiva, satisfied by her prayers, appeared before parvati and asked her to go to a place on the Earth, near the kaveri river and worship him from there. Parvati arrived at the place which is famous for the royal elephants which are referred to as "Maha Padmam". Due to the abundance of the royal elephants, the place was known as "Gajaaranyam" (Gaja - Elephant, aaranyam - forest) or forest full of royal elephants.
Parvati took handful of water from the river and left them on the ground, thinking about Shiva. The water stood in the place where she left them on the ground in the form of a shiva lingam. She then performed pooja for the same. Shiva became happy and he made parvati to stay in the kshetra as Akilandeswari and bless the devotees who come to worship them.
Since she created the lingam using water, the temple is designated as appu sthalam among the panch bhootha sthalaas.
Even today to comemorate the event of Akilandeswari worshipping Jambukeswara, everyday, one of the temple priest use to decorate himself in a saree (signifying Parvati) and offer pooja to Jambukeswara during the uchi kaala (afternoon time). The garba griha (sanctum) of Jambukeswara use to be wet always. It is belived that the water from the river kaveri use to be there always.