  Localization transitions as a function of temperature require a many-body
mobility edge in energy, separating localized from ergodic states. We argue
that this scenario is inconsistent because local fluctuations into the ergodic
phase within the supposedly localized phase can serve as mobile bubbles that
induce global delocalization. Such fluctuations inevitably appear with a low
but finite density anywhere in any typical state. We conclude that the only
possibility for many-body localization to occur are lattice models that are
localized at all energies. Building on a close analogy with a model of assisted
two-particle hopping, where interactions induce delocalization, we argue why
hot bubbles are mobile and do not localize upon diluting their energy.
Numerical tests of our scenario show that previously reported mobility edges
cannot be distinguished from finite-size effects.
