  The boundary of a 2D topological superconductor can be modeled by a conformal
field theory. Here we demonstrate the behaviors of this high level description
emerging from a microscopic model at finite temperatures. To achieve that, we
analyze the low energy sector of Kitaev's honeycomb lattice model and probe its
energy current. We observe that the scaling of the energy current with
temperature reveals the central charge of the conformal field theory, which is
in agreement with the Chern number of the bulk. Importantly, these currents can
discriminate between distinct topological phases at finite temperatures. We
assess the resilience of this measurement of the central charge under coupling
disorder, bulk dimerisation and defects at the boundary, thus establishing it
as a favorable means of experimentally probing topological superconductors.
