  Frustrated quantum spin systems such as the Heisenberg and Kitaev models on
various lattices, have been known to exhibit various exotic properties not only
at zero temperature but also for finite temperatures. Inspired by the
remarkable development of the quantum frustrated spin systems in recent years,
we investigate the finite-temperature properties of the $S=1/2$
Kitaev-Heisenberg models on kagome and triangular lattices by means of
finite-temperature Lanczos methods with improved accuracy. In both lattices,
multiple peaks are confirmed in the specific heat. To find the origin of the
multiple peaks, we calculate the static spin structure factor. The origin of
the high-temperature peak of the specific heat is attributed to a crossover
from the paramagnetic state to a short-range ordered state whose static spin
structure factor has zigzag or linear intensity distributions in momentum
space. In the triangular Kitaev model, the "order by disorder" due to quantum
fluctuation occurs. On the other hand, in the kagome Kitaev model it does not
occur even with both quantum and thermal fluctuations.
