Reduced-order modelling (ROM) is essential for enabling real-time prediction and control of laser welding processes, where high-fidelity full-order models (FOMs) are computationally expensive. This study investigates whether intrusive projection-based and non-intrusive input–output ROM approaches can preserve the dominant laser-power-to-temperature dynamics of AA1050 laser welding while maintaining computational efficiency and generalization across different operating conditions. Eight cases were investigated, including linear thermal behavior, temperature-dependent properties, phase change, heat losses, moving heat sources and fluid-flow effects. Linear full order state-space models (SSFOM) accurately reproduced FOM responses, achieving normalized RMSE below 0.6% for linear FOMs. Balanced truncation provided the best accuracy-to-complexity trade-off, retaining near FOM accuracy with 31–36 states when asymptotically stable models could be extracted. Transfer function models offered the lowest computational cost and widest applicability but showed reduced accuracy beyond the training window. It was also the only approach applicable to all investigated formulations, including cases for which internal state-space matrices could not be reliably extracted. Modal truncation was simpler to construct but required 2000 retained modes and inherited marginal stability under temperature-dependent fixed-beam conditions. The results describe clear trade-offs among accuracy, stability, compactness, computational cost and applicability and establish foundation for developing a framework for real-time laser welding control based on ROM.