The gas-liquid separation performance of corrugated plates in steam-water separators of pressurized water reactor secondary loops is affected by system pressure, working fluid velocity and geometric structure. The dynamic variations of these factors induce strongly nonlinear thermo-fluid coupling effects, which impose strict requirements on the accurate prediction of flow and temperature fields. Traditional Physics-informed Neural Networks (PINNs) suffer from the generalization bottleneck of "one geometry, one training; one working condition, one iteration". Moreover, the inherent structural constraints of MLP result in insufficient fitting accuracy for strongly nonlinear laws, making it difficult to meet the prediction requirements of variable-geometry structures.  This paper applies the PI-DeepONet architecture to this field. Relying on the infinite-dimensional mapping capability of Deep Operator Network (DeepONet) to overcome PINN's operator-level generalization limitation, it completes preliminary thermo-fluid field prediction with Fourier encoding. A serial "prediction-error compensation" architecture is proposed. An error compensation module integrating Fourier Neural Operator (FNO) and U-shaped Convolutional Encoder-Decoder Network (U-Net) is designed to explicitly learn error distributions, combined with magnitude-adaptive loss weights and Y-direction location-aware weights to enhance nonlinear feature learning. Experiments show that the training dataset size of the model is reduced from 1e3 to 1e2, significantly cutting training costs. The framework achieves both excellent fitting accuracy and cross-untrained geometry/condition generalization capability in strongly nonlinear thermo-fluid coupling prediction. This method realizes operator-level generalized prediction of variable-geometry multi-physics fields in nuclear thermal equipment, and the introduction of engineering measured data can further improve its engineering applicability.