  Finite-temperature ($T$) properties of a Kitaev model defined on a honeycomb
lattice are investigated by a quantum Monte Carlo simulation, from the
viewpoint of fractionalization of quantum $S=1/2$ spins into two types of
Majorana fermions, itinerant and localized. In this system, the entropy is
released successively at two well-separated $T$ scales, as a clear indication
of the thermal fractionalization. We show that the high-$T$ crossover, which is
driven by itinerant Majorana fermions, is closely related with the development
of nearest-neighbor spin correlations. On the other hand, the low-$T$ crossover
originates in thermal fluctuations of fluxes composed of localized Majorana
fermions, by which the spectrum of itinerant Majorana fermions is significantly
disturbed. As a consequence, in the intermediate-$T$ range between the two
crossovers, the system exhibits $T$-linear behavior in the specific heat and
coherent transport of Majorana fermions, which are unexpected for the Dirac
semimetallic spectrum in the low-$T$ limit. We also show that the flux
fluctuations tend to open an energy gap in the Majorana spectrum near the
gapless-gapped phase boundary. Our results indicate that the fractionalization
is experimentally observable in the specific heat, spin correlations, and
transport properties.
