  The formation of a heavy Fermi liquid in metals with local moments is
characterized by multiple energy and temperature scales, most prominently the
Kondo temperature and the coherence temperature, characterizing the onset of
Kondo screening and the emergence of Fermi-liquid coherence, respectively. In
the standard setting of a wide conduction band, both scales depend
exponentially on the Kondo coupling. Here we discuss how the presence of flat,
i.e., dispersionless, conduction bands modifies this situation. Focussing on
the case of the kagome Kondo-lattice model, we utilize a parton mean-field
approach to determine the Kondo temperature and the coherence temperature as
function of the conduction-band filling $n_c$, both numerically and
analytically. For $n_c$ values corresponding to the flat conduction band
located at the Fermi level, we show that the exponential is replaced by a
linear dependence for the Kondo temperature and a quadratic dependence for the
coherence temperature, while a cubic law emerges for the coherence temperature
at $n_c$ corresponding to the band edge between the flat and dispersive bands.
We discuss implications of our results for pertinent experimental data.
