There are many legends behind Srikalahasti temple, which is one of the Panchaboota Kshetras. But none of these legends explain origin of Vayu Lingam which is believed to be "Swayambhu" (self-manifested).
Famous among of all legends is story of three staunch devotees "Sri (spider), Kala (serpent) and Hasti (elephant)". But this legend says that they worshiped already existed lingam. Same is the case with other stories such as Bhakta Kannappa, penance of Parvati and Markandeya.
According to this wiki page,
It is said that Lord Shiva, after Bhasmasura was killed with the help of Lord Maha Vishnu, performed the Tandava Dance and then performed the "Rudra Yagna" for the betterment of humanity. The place where the Rudra Yagna was performed is where the "Sri Kalahasti" Temple stands now.
Does this dance of Rudra has anything to do with this temple? What is the exact legend behind origin of SriKalaHasti temple?
What is the meaning of Vayu Lingam? At Arunachalam (Tiruvannamala), Lord Shiva appeared as "Jyoti" or fire column, so lingam there is called as Agni Lingam. Similarly, empty space at Chidambaram is worshiped as "Akasa Lingam". So, what is the meaning of "Vayu Lingam" at Srikalahasti temple?