  We investigated the double-exchange spin ice model on a kagom\'e lattice by
Monte Carlo simulation in order to study a mechanism for lifting the degeneracy
in frustrated electron systems. We show specific heat and vector spin chirality
data on a finite lattice. Specific heat has a double-peak structure: A broad
peak and a sharp peak are at $k_{\rm B}T/t \sim 0.15$ and 0.015, respectively,
where $t$ is the transfer integral of electrons. The broad peak corresponds to
a crossover to the spin ice-like state, on the other hand, the sharp one a
transition to a dodecagonal spin cluster (dodecamer) state. We discuss the
interplay between the formation of the dodecamer state and the lifting of the
macroscopic degeneracy.
