The idea of fire in hell in the Christian context stems back to early Judaism. For some context, the Israelites believed they were given promised land by God; however, the land was occupied by various different peoples when the Israelites arrived. This included the Canaanites, who were deemed wicked for their religious practices. It was said by the Israelites that the valley of Hinnom was where the Canaanites performed child sacrifices in the name of their god Molech. By the time of Jesus’ teachings, the valley (located not far from Jerusalem) had become a place where trash and corpses were disposed. To destroy the bodies and the rubbish, they were often set on fire and brimstone (sulphur) was added so that the fires would not go out. Due to the Canaanites being one of the prime examples in Judaism of a people that denied God and went against his will, in Jesus’ teachings of heaven and hell he used this location as an example of what happens to those who defy God. As a result, the concept of fire and brimstone being a punishment for evildoers became prevalent in Christianity.

If you want to read more about the origins and history of religious concepts, there is an article in Numen (a journal on the History of Religions) that covers the origins of the Christian concept of hell.

Kyrtatas, D. (2009). The Origins of Christian Hell. Numen, 56(2/3), 282-297. http://www.jstor.org/stable/27793793