  Temperature evolution of the spin correlation and excitation spectrum is
investigated for a Kitaev model defined on a decorated honeycomb lattice by
using the quantum Monte Carlo simulation in the Majorana fermion
representation. The ground state of this quantum spin model is given by two
kinds of chiral spin liquids: one is topologically trivial with Abelian anyon
excitations, and the other is topologically nontrivial with non-Abelian anyon
excitations. While lowering temperature, the model exhibits several crossovers
in the paramagnetic state, which originate from the fractionalization of
quantum spins into Majorana fermions, in addition to a phase transition
associated with time reversal symmetry breaking. We show that the spin
correlation develops around the crossover temperatures, whereas it shows a
slight change at the critical temperature, as in other Kitaev-type models. We
also calculate the excitation spectrum in terms of Majorana fermions, and find
that the excitation gap in the non-Abelian phase is fragile against thermal
fluctuations of the $Z_2$ fluxes, while that in the Abelian phase remains open.
