Robotized manufacturing processes such as Wire Arc Additive Manufacturing (WAAM) and Laser Wire Additive Manufacturing (LWAM) are inherently multi-physics and governed by partial differential equations (PDEs). Classical numerical solvers (FEM, FDM, FVM) provide accuracy but are often too slow for mechatronic use cases like real-time monitoring, model-predictive control, or high-fidelity digital twins. This paper demonstrates how Physics-Informed Neural Networks (PINNs) can approximate transient thermal fields in LWAM by minimizing PDE and boundary residuals directly, eliminating the need for meshing or time stepping at inference. We provide a reproducible PINN implementation, an ONNX-exportable inference wrapper for deployment, and a companion ONNX validator that confirms faithful model export by comparing ONNX predictions against the trained PyTorch model outputs (MAE <0.001∘C).