  We derive and calculate thermal transport coefficient for a quantum Hall
system in the linear response regime, and show that they are exponentially
small in the bulk, in contrast to the quantized value of the charge Hall
coefficient, thus violating Wiedemann-Franz law. This corroborates earlier
reports about the essential difference between the charge and thermal quantum
Hall effect, that originates from the different behavior of the corresponding
$U(1)$ and gravitational anomalies. We explicitly calculate the bulk currents
when a temperature profile is applied within the bulk, and show that they are
proportional to the second derivative of the respective gravitational potential
(tidal force), and nonuniversal, in contrast to the charge current which is
proportional to the first derivative of the electrochemical potential.
