A widely held belief is that anelasticity can contribute significantly to seismic wave-speed variations in the lower mantle. In particular it has been argued that anelasticity can strongly increase the sensitivity of VS to temperature, and that anelasticity may also increase VS relative to VP (as measured by the parameter RS/P = dln VS/dln VP). If true, this could significantly reduce or, in some cases, eliminate the need to explain seismic signals in the mantle with chemical heterogeneity, and that most of the variation in seismic velocities in the lower mantle could be attributed to temperature alone. We re-visit this view and find that a strong anelastic effect is unlikely in the Earth's lower mantle. Given the present knowledge of the properties of perovskite under lower mantle conditions, we find it unlikely that anelasticity can affect dln VS/d T by more than about 30%, and it is most likely less than 20%. We also find that the probable upper bound on dln VS/dln VP due to thermal variations is about 1.8 in the shallow lower mantle, and about 2.1 in the deeper lower mantle. We conclude, therefore, that anelasticity cannot be invoked to significantly reduce or remove interpretations of lower mantle chemical heterogeneity based on large-scale seismic wave-speed variations.