A  finite element representation modelling transient heat conduction of gas tungsten arc welding of stainless steel is used to evaluate different methods for model order reduction. The focus is on establishing a linear low-order model of the dynamic  relation between the welding current and the temperature measured by a radiation pyrometer. The objective of this low-order model is to design a model-based feedback controller and to investigate the consequences of applying feedback control of the process. Three different approaches for model reduction have been evaluated, namely the Krylov subspace method for moment    matching, balanced truncation and parametric system identification. The study provides a knowledge base for the selection of model order reduction methods when dealing with large-scale systems like finite element models of transient heat conduction, and it recommends parametric system identification. It renders sufficient approximations for controller design, no linearization of the finite element model is required, and there is no limit on degrees of freedom of the finite element model.