  We study the dynamical thermal conductivity of the two-dimensional Kitaev
spin-model on the honeycomb lattice. We find a strongly temperature dependent
low-frequency spectral intensity as a direct consequence of fractionalization
of spins into mobile Majorana matter and a static $\mathbb{Z}_{2}$ gauge field.
The latter acts as an emergent thermally activated disorder, leading to the
appearance of a pseudogap which partially closes in the thermodynamic limit,
indicating a dissipative heat conductor. Our analysis is based on complementary
calculations of the current correlation function, comprising exact
diagonalization by means of a complete summation over all gauge sectors, as
well as a phenomenological mean-field treatment of thermal gauge fluctuations,
valid at intermediate and high temperatures. The results will also be
contrasted against the conductivity discarding gauge fluctuations.
