Aiming at the high-order harmonic problems occurred in the actual operation of 500kV connected transformer, a 3D finite element model of the connected transformer is established, and magnetic flux of the iron core, magnetic leakage flux of the tank wall and the frame clamps under fundamental wave and harmonic condition were calculated, and a magnetic-thermal coupling method was used to calculate the temperature field distribution and hot spot temperature of the iron core and clamps.Results show that, under high-order harmonic conditions, magnetic flux of the iron core and magnetic leakage flux of the tank wall and the frame clamps increase significantly. The magnetic leakage in the middle part of the tank is large, so the magnetic shielding at this part should be strengthened. Under high-order harmonic conditions, the temperature of the iron core and frame clamps also increase significantly, and hot spot temperature of the iron core and clamps increases 6.7℃ and 1.7℃, respectively. Therefore, the monitoring should be strengthened in the operation process to avoid the insulation damage caused by excessive local temperature in the connection transformer under harmonic conditions. The results of this paper provide references for the optimal design and actual operation of the connected transformer.