  A heat conduction equation on a lattice composed of nodes and bonds is
formulated assuming the Fourier law and the energy conservation law. Based on
this equation, we propose a higher-order topological heat conduction model on
the breathing kagome lattice. We show that the temperature measurement at a
conner node can detect the corner state which causes rapid heat conduction
toward the heat bath, and that several-nodes measurement can determine the
precise energy of the corner states.
