While nothing has been revealed about his life nor his struggles as the Avatar, the only confirmed fact about the unnamed fire Avatar is that he preceded Avatar Yangchen. His abilities are nothing short of exemplary, as he has been seen bending the lava from multiple volcanoes at one time, suggesting that he was extremely proficient in both earthbending and firebending.
Nothing is known about his death; however, after he passed, the Avatar Spirit was reincarnated into an Air Nomad, Yangchen.
Appearances in Aang's life
When Aang inadvertently entered the Avatar State during a retreat to GeneralFong's fortress as a result of his anger when Fong put Katara's life at risk in hopes it would force Aang into the Avatar State, Aang was taken by Avatar Roku on a journey to the Spirit World. There, Roku showed the young airbender flashbacks of previous Avatars empowered by the Avatar State, including the unnamed fire Avatar erupting four adjoining volcanoes with the use of enhanced firebending and earthbending.
During Avatar Aang's battle at Wulong Forest against Phoenix KingOzai, the unnamed fire Avatar made another appearance where he was seen in Aang's vision alongside a line of Avatars when Aang unlocked the seventh chakra and immediately entered the Avatar State, resulting from an impact with a jutting rock.
Appearances in Korra's life
The unnamed fire Avatar was present along with several other Avatars when Aang passed on the knowledge of energybending to Korra, representing the connection she had made with her spiritual side.
Although he was only seen very briefly, it is evident that the unnamed fire Avatar had complete control of the Avatar State, able to enter and exit it at will. He was seen controlling a number of small volcanoes with the use of his abilities, though the exact extent of his power remains unexplored.