Fusion welding remains the most common and convenient fabrication method for large, thinplate welded structures. However, the resulting tendency to out-of-plane distortion exacts severe design and fabrication penalties in terms of poorer buckling performance, lack of fairness in external appearance, poor fit-up and frequent requirements for expensive rework. There are several ways to mitigate welding distortion and this study concentrates on the use of cryogenic CO2 cooling to reduce distortion. A feasible combination of welding process and cooling parameters, was investigated computationally and the resulting effects on final deformation were predicted. Three different computational strategies were developed and applied to butt-welding and fillet-welding processes, with and without the inclusion of cryogenic cooling. In the first method, a fully transient, uncoupled thermo-elastoplastic model was investigated. This method is comprehensive but not readily applicable to predict welding distortions in complex, industrial-scale, welded structures, due to the large computational requirement. More computationally efficient models are needed therefore and two further models of this type are suggested in this study. The results show good agreement between the different models, despite substantial differences in computational budget. In butt-welded plates, a significant decrease in out-of-plane distortion is obtained when cryogenic cooling is applied. In fillet-welded plates, cooling had much less effect on welding distortion. This was largely due to the size and configuration of the test case assemblies and the fact that the attached stiffener greatly increased the overall stiffness and resistance to contraction forces