Logi means fire in German and Norwegian. So Logi, the god of fire, makes a cameo appearance in one story of the Prose Edda. However, Logi is running along side Loki, the trap god. So I think this is a Snorri Sturluson pun. The association between fire and Loki is a mere play on words, not read anywhere in the Prose Edda.
Loki the trickstermost probably orignated from the old Norwegian word for ‘chain’. So the closest English cognate to Loki is ‘lock’ rather than ‘fire’. Some scholars think that the word for chain got associated with traps.
Loki is the god of traps. Loki IS NOT the god of fire. None of his children are fire gods. They are gods of death. The iconography may be that death is the greatest of all traps.
Loki is imprisoned in the underworld, tortured with poison, has his mouth sewed closed, caught in a fishing net, stuck on an eagles behind, and grabbed by just about everyone. His three horrible children are chained, tied up, and buried underground. His less famous children are gutted to provide cords for tying him up. Loki is NEVER burned, however. Nor does he burn anybody. The common theme in most Loki stories is entrappment.
Loki is trapped in some way some way in many of his stories.. All his children get trapped in some way. He entraps others. In many of his stories, he turns into an aquatic animal which is somehow trapped. He never seems to set a fire in the mythology.
Wagner called Loki the fire god. However, I think that was Wagnerian license. Wagner is not consistent with authentic mythology, especially not the Prose Edda. There is a song in one of Wagner’s operas referring to the ‘Chain of Fire’. However, I think this is a mere play on words.
A hearth is a fireplace, as /u/edselford says. A stone like this one is used in forges and protects the bellows from the heat while channeling the airflow.
The stone is identified as a hearth stone; the nozzle of the bellows would be inserted into the hole in the front of the stone, and the air produced by the bellows pushed flame through the top hole, all the while the bellows were protected from the heat and flame. The stone may point to a connection between Loki and smithing and flames. According to Hans Jørgen Madsen, the Snaptun Stone is “the most beautifully made hearth-stone that is known.” The stone is housed and on display at the Moesgård Museum near Aarhus, Denmark
One example of Loki’s association with fire is his eating contest with Lue (‘Flame’) during his visit to Utgard-Loki.