The voltage across a 77‐kV‐class transmission line surge arrester (TLSA) and the heat in the TLSA have been computed using the finite‐difference time‐domain (FDTD) method for a lightning current having a magnitude of 50 kA, a risetime of 1 μs, and a half‐peak width of about 100 μs. The TLSA is represented with series‐connected‐nine ZnO elements, each of which has a length of 36 mm and a diameter of 32 mm. The ZnO element is represented with many 2 × 2 × 2 mm cubic cells, each of which has a nonlinear resistivity in each of the x‐, y‐, and z‐directions dependent on the electric field in each direction and the temperature in each cell. From the spatial and temporal distributions of FDTD‐computed heat in the TLSA, the spatial and temporal distributions of thermal stress in the TLSA have been computed using the finite‐element method. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.