The linear behavior of thermal transport has been widely explored, both theoretically and experimentally. On the other hand, nonlinear response not fully discussed. In light vector potential theory [Tatara, Phys. Rev. Lett. 114, 196601 (2015)], we develop a general formulation to calculate dynamic responses. DC limit, recover well-known Mott relation Wiedemann-Franz (WF) law at order response, ...