I wonder to what extent nuclear would be an option, given the relative abundance of previously-enchriched fuel now sitting around as waste, and an post-apocalyptic willingness to engage in high-risk, high-reward behavior... I suspect that there would be people and places that would be OK with the impacts of leaky, poorly shielded nuclear piles if it meant seemingly-endless sources of high heat independent of the need for piles of charcoal.
At the very least, in the right hands that idea could probably make for an interesting short story.
At the very least, in the right hands that idea could probably make for an interesting short story.