The existing heat dissipation research on double disk magnetic couplers ignores the coupling influence of electromagnetic temperature–stress and other multiphysics fields, and the error between the calculation and analysis results and the measured values is large. Therefore, a multi-parameter optimization method for heat dissipation structures of double disk magnetic couplers based on orthogonal experimental design is proposed. Based on the double disk magnetic coupler model, a three-dimensional finite element model based on fluid–solid–heat coupling is established, with the axial air gap length, input motor speed, the thickness of the permanent magnet in the magnetizing direction, the thickness of the copper plate, the number of fins of the heat dissipation plate and the length of the fins of the heat dissipation plate as design variables. Six-factor and three-level simulation experiments are designed with the minimum temperature of the heat dissipation plate as the objective function, and additionally, orthogonal experiments were designed according to the actual working conditions by selecting the optimal combination of parameters and modifying the model to perform physical tests. The results show that the variables that have the most significant impact on heat dissipation performance from high to low are as follows: axial air gap length, input motor speed, the length of the fins of the heat dissipation plate, the thickness of the permanent magnet in the magnetizing direction, the number of fins of the heat dissipation plate and the thickness of the copper plate. The increase in axial air gap length can effectively reduce the temperature rise, and the maximum decrease can reach 9.76%. Under the same conditions, the input motor speeds are set to 300 r/min, 400 r/min, 500 r/min, 600 r/min and 700 r/min, respectively, and the simulation results are in good agreement with the physical test results, with a maximum error of 4.8%. The error between the simulation result and the physical test result is only 1.9% under the optimal combination of parameters obtained by the orthogonal experiment, which verifies the correctness of the optimization model. In conclusion, the study is of reference significance for the parameter optimization of the heat dissipation structure of the double disk magnetic coupler.