Who was Nammazhvar?

The divine tamarind tree adjoining the Gopura over the Nammalwar temple in Alwartirunakari (also known as Tirukkurugur), Tamil Nadu. It is believed that the Alwar as a child, got up and climbed into a hole in tamarind, sat in the lotus position, and began to meditate. It appears he was in this state for as long as sixteen years when a Tamil poet and scholar in North India named Madhurakavi Alvar saw a bright light shining to the south and followed it until he reached the tree where the boy was residing. Unable to elicit any reaction from the child, he asked him a riddle: "If the small is born in a dead's body (or stomach), what will it eat and where will it stay?" meaning, if the subtle soul is embodied in the gross body, what are its actions and thoughts? Nammalvar broke his lifelong silence and responded, "That it will eat, it will rest!" meaning that if the soul identifies with the body, it will be the body but if it serves the divine, it will stay in Vaikuntha and eat(think) of God. Madhurakavi Alvar realized the divinity of this child. Vaishnavite saint Nammazhvar, although he had an earthly sojourn, knew no hunger or thirst.

Those in Sri Vaikuntha are the ones who do not experience the pangs of hunger or thirst. But those in Sri Vaikuntha do not come down to Earth.