Recent seismic imaging across the Rio Grande rift, western United States, revealed unexpected structures in the underlying mantle. Low seismic wave velocity anomalies below the Rio Grande rift have been interpreted as being partially of melt origin, and high-velocity structures below the western Great Plains have been proposed to be the result of small-scale convection, i.e., cold downwelling lithospheric material with probably a compositional contribution. We perform a dynamic test of these interpretations using a passive rift model for isochemical convection. The models self-consistently produce a rift localized at approximately the right distance from the border to the nearby thicker Great Plains lithosphere. With realistic upper mantle rheologies, small-scale convection forms, aided by the lithospheric step. The resulting thermal anomalies produce seismic low-velocity anomalies below the rift of amplitudes similar to those imaged seismically, requiring the presence of only small amounts of melt. The lateral extent of the observed low velocities below the Rio Grande rift is as in the models, where it is controlled by the spacing between downwelling limbs of the small-scale convection. The fast velocity structure below the western Great Plains can be produced by cold downwelling lithosphere. The thermal rifting models can predict the amplitudes and size of the main seismic anomalies; compositional heterogeneity may contribute to some of the smaller features observed.