We show that a volatile liquid drop placed at the surface of a nonvolatile liquid pool warmer than the boiling point of the drop can be held in a Leidenfrost state even for vanishingly small superheats. Such an observation points to the importance of the substrate roughness, negligible in the case considered here, in determining the threshold Leidenfrost temperature. A theoretical model based on the one proposed by Sobac et al. [Phys. Rev. E 90, 053011 (2014)] is developed in order to rationalize the experimental data. The shapes of the drop and of the liquid substrate are analyzed. The model notably provides scalings for the vapor film thickness profile. For small drops, these scalings appear to be identical to the case of a Leidenfrost drop on a solid substrate. For large drops, in contrast, they are different, and no evidence of chimney formation has been observed either experimentally or theoretically in the range of drop sizes considered in this study. Concerning the evaporation dynamics, the radius is shown to decrease linearly with time whatever the drop size, which differs from the case of a Leidenfrost drop on a solid substrate. For high superheats, the characteristic lifetime of the drops versus the superheat follows a scaling law that is derived from the model, but, at low superheats, it deviates from this scaling by rather saturating.