There are many temples in South India dedicated to Shri Muneshwara Swamy.
On Googling only this much information was found.
Lord Muneshwaraan, who is a Hindu God, worshipped as a family deity in most Shaivite families in India.
Who is this deity? What is his story?
Muneshvara is a well-known folk deity worshipped in Tamil Nadu. Actually, his name was based on the name "Munishvara".
As per a folklore, he was created by Lord Shiva for save people when Veerabhadra going to destroy Prajapati Daksha's Yajna.
However, The name of Munishvara also mentioned in this chapter of Skanda Purana.
21-32. Viṣṇu himself, the Lord of the heart, performs the Japa of Maheśvara. So also do Gandharvas, celestial damsels, Maruts, Mārutas, Viśvedevas, Pitṛs, Moon, Sun, Marīci, Atri, Aṅgiras, Pulastya, Pulaha, Kratu, Pracetas, Vasiṣṭha, Bhṛgu, Nārada, Cyavana, Gālava, the great sage Vāmadeva, Vālakhilyas, Gandhāras, Tṛṇabindu, Jājali, Uddālaka, Ṛṣyaśṛṅga, Vasiṣṭha, Sanandana, Śukra, Bharadvāja, Vātsya, Vātsyāyana, Agasti, Mitra, Varuṇa, Viśvāmitra, Munīśvara, Gautama, Pulastya, Paulastya, Pulaha, Kratu, Sanātana, Kapila, Vahni, Pañcaśikha and many other sages of esteemed holy rites. All the Devas, sages, ascetics, human beings, Yogīndras, Pitṛs, along with Pitāmahas etc. stay in Asmāhaka. There is no doubt about it.
I hope it helps.
