This paper considers the problem of reconstructing visually realistic 3D models of fire from a very small set of simultaneous views (even two). By modeling fire as a semi-transparent 3D density field, we show that fire reconstruction is equivalent to a severely under-constrained computerized tomography problem, for which traditional methods break down. Our approach is based on the observation that every pair of photographs of a semi-transparent scene defines a unique density field, called a Flame Sheet, that (1) concentrates all its density on one connected, semi-transparent surface, (2) reproduces the two photos exactly, and (3) is the most spatially-coherent density field that does so. From this observation, we reduce fire reconstruction to the convex combination of sheet-like density fields, each of which is derived from the Flame Sheet of two input photos. Experimental results suggest that this method enables high-quality view extrapolation without over-fitting artifacts.