The double-ellipsoidal heat power density model proposed by Goldak, has been widely used as the basis for modelling heat transfer in arc welding operations for more than thirty years. This approach has proved to be extremely effective for a wide range of arc welding operations. However, the application of a double-ellipsoidal heat power density distribution is less appropriate for keyhole-laser or electron-beam welding operations, or in situations where arc welding takes place within deep narrow grooves. In this paper the double-ellipsoidal distribution is extended to a double-ellipsoidal-conical heat power density model in order to accurately describe transient temperature fields for a wider range of geometries and welding processes. The new extended model was validated through comparing predicted welding thermal cycles with those measured for a single pass electron beam weld, as well as those measured in a multi-pass narrow groove gas-tungsten-arc weld. In both cases, excellent agreement was obtained between predicted and measured thermal transients.