The transient temperature fields induced by welding processes largely determine the size of the fusion and heat-affected zones, the microstructures, residual stresses and distortion both in the vicinity of the weld and in the final component as a whole. An accurate prediction of these fields relies heavily on the representation of the welding heat source, both in space and in time.The double-ellipsoidal heat source model proposed by Goldak and co-workers has been widely used to simulate the heat transferred from an electric arc to a component and to compute the induced transient temperature fields. This double-ellipsoidal distribution has worked well for many welding applications, but it is less appropriate when representing the heat transfer at the base of a groove whose width is narrow in relation to its depth. Similarly the conical heat source models used to represent the electron beam welding process, when applied in keyhole mode, are less appropriate when the keyhole terminates within the component, such as in the case of a partial penetration weld.In this work, the double-ellipsoidal heat source model is extended, and alternatives presented, to account for a wider set of welding scenarios, including narrow weld groove geometries and keyhole welding scenarios. A series of mathematically robust novel heat source models is presented and the models are validated against experimental data obtained during the application of various welding processes to an important grade of pressure vessel steel, namely SA508 Grade 3 class 1 steel.The calculation of the transient temperature fields during welding is extremely computationally expensive using numerical methods. Where available, and appropriate, analytical solutions are presented for these novel welding heat source models, coupled with analytical methods for accounting for time dependent heat input rates, to not only reduce computational cost but also to achieve precise predictions of the temperature fields. This, in turn, has the potential to contribute to improvements in safety assessments on critical welded infrastructure through improved predictions for the evolution of microstructure, mechanical properties and the levels of residual stress and distortion in welded joints.