We explore the phenomenology of a class of models where the dark matter particle can inelastically up-scatter to a heavier excited state via off-diagonal dipolar interactions with the interstellar plasma (gas or free electrons). The heavier particle then rapidly decays back to the dark matter particle plus a quasi-monochromatic photon. For the process to occur at appreciable rates, the mass splitting between the heavier state and the dark matter must be comparable to, or smaller than, the kinetic energy of particles in the plasma. As a result, the predicted photon line falls in the soft X-ray range, or, potentially, at arbitrarily lower energies. We explore experimental constraints from cosmology and particle physics, and present accurate calculations of the dark matter thermal relic density and of the flux of monochromatic X-rays from thermal plasma excitation. We find that the model provides a natural explanation for the observed 3.5 keV line from clusters of galaxies and from the Galactic center, and is consistent with null detections of the line from dwarf galaxies. The unique line shape, which will be resolved by future observations with the Hitomi (formerly Astro-H) satellite, and the predicted unique morphology and target-temperature dependence will enable easy discrimination of this class of models versus other scenarios for the generation of the 3.5 keV line or of any other unidentified line across the electromagnetic spectrum.