  We revisit a theory of heat transport in the light of a gauge theory of
gravity and find the proper heat current with a corresponding gauge field,
which yields the natural definitions of the heat magnetization and the
Kubo-formula contribution to the thermal conductivity as torsional responses.
We also develop a general framework for calculating gravitational responses by
combining the Keldysh and Cartan formalisms. By using this framework, we
explicitly calculate these two quantities and reproduce the Wiedemann-Franz law
for the thermal Hall conductivity in the clean and non-interacting case.
Finally, we discuss an effective action for the quantized thermal Hall effect
in $(2 + 1)$-D topological superconductors.
