The architectures of debris disks encode the history of planet formation in these systems. Studies of debris disks via their spectral energy distributions (SEDs) have found infrared excesses arising from cold dust, warm dust, or a combination of the two. The cold outer belts of many systems have been imaged, facilitating their study in great detail. Far less is known about the warm components, including the origin of the dust. The regularity of the disk temperatures indicates an underlying structure that may be linked to the water snow line. If the dust is generated from collisions in an exo-asteroid belt, the dust will likely trace the location of the water snow line in the primordial protoplanetary disk where planetesimal growth was enhanced. If instead the warm dust arises from the inward transport from a reservoir of icy material farther out in the system, the dust location is expected to be set by the current snow line. We analyze the SEDs of a large sample of debris disks with warm components. We find that warm components in single-component systems (those without detectable cold components) follow the primordial snow line rather than the current snow line, so they likely arise from exo-asteroid belts. While the locations of many warm components in two-component systems are also consistent with the primordial snow line, there is more diversity among these systems, suggesting additional effects play a role.