  We study the thermal conductivity in the excitonic insulator using a simple
quasi one-dimensional two-band model consisting of electron and hole bands with
the Coulomb interactions between these bands. Based on the linear response
theory within a mean-field scheme, we develop a method to identify the
contributions to thermal conductivity driven by excitonic insulator. It is
found that there is an additional heat current operator owing to the excitonic
phase transition, and that it gives contributions to thermal conductivity which
are not expressed in the form of Sommerfeld-Bethe relations written in the form
of an imaginary-time derivative of the electric current operator. Finally, we
discuss the relationship between the newly-found additional contribution and
the heat current carried by excitons.
