A key characteristic of wet spinning process is the complex coupling of thermo-elastic effects, fluid–structure interaction (FSI), and dynamic interplay, thereby achieving the stretching and cooling of filament bundle in the coagulation bath. These coupled mechanisms fundamentally govern filament solidification behavior and the resulting material properties. This study proposes a thermo–fluid–structure multi-physics coupling framework based on the Absolute Nodal Coordinate Formulation (ANCF). Through systematic physical and mathematical characterization of the wet spinning process, an ANCF beam-element geometric model of the filament bundle is constructed, which explicitly incorporates the nonlinear and time-dependent evolution of elastic modulus during solidification. A displacement–temperature coupling formulation is established to derive the fully coupled governing equations of the multi-physics system. The incompressible Navier–Stokes equations are solved via the Weak Galerkin (WG) finite element method to obtain the three-dimensional velocity field in the coagulation bath. Key physical effects, including heat conduction inside the filament bundle, interfacial heat exchange, rheological resistance, temperature-dependent modulus evolution, and strain-rate strengthening effects are integrated into the formulation. Furthermore, a dimensional-reduction strategy–combining Taylor series expansion, piecewise linearization, and free-surface modal synthesis is introduced to derive the coupled dynamic equations of the multi-body system. The proposed framework captures the coupled mechanisms of thermo-flexural interaction, fluid–structure coupling, and dynamic modulus evolution, enabling high-fidelity numerical simulation of the extrusion–cooling–solidification sequence of the filament bundle.