Heat conduction of the breathing Kagome lattice is discussed in relation to the anomalous heat-carrying corner states due to higher-order topology. Especially the use of the effective Hamiltonian for the corner states is proposed and its validity is demonstrated. The paper “Higher-order topological heat conduction on a lattice for detection of corner states” by Takahiro Fukui, Tsuneya Yoshida, and Yasuhiro Hatsugai has been accepted for publication in Phys. Rev. E on 13 July 2023 and published on 7 Aug. 2023. Have a look at it! Also, see arXiv:2303.08402