  Unconventional features of the magnetization curve at zero temperature such
as plateaus or jumps are a hallmark of frustrated spin systems. Very little is
known about their behavior at non-zero temperatures. Here we investigate the
temperature dependence of the magnetization curve of the kagome lattice
antiferromagnet in particular at 1/3 of the saturation magnetization for large
lattice sizes of up to N=48 spins. We discuss the phenomenon of asymmetric
melting and trace it back to a combined effect of unbalanced magnetization
steps on either side of the investigated plateau as well as on the behavior of
the density of states across the plateau. We compare our findings to the
square-kagome lattice that behaves similarly at low temperatures at zero field,
but as we will demonstrate differently at 1/3 of the saturation magnetization.
Both systems possess a flat one-magnon band and therefore share with the class
of flat-band systems the general property that the plateau that precedes the
jump to saturation melts asymmetrically but now with a minimal susceptibility
that bends towards lower fields with increasing temperature.
