Electrical machines are progressively being employed in an ever-increasing number of safety-critical applications (e.g. aerospace and automotive), which demand high performance as well as reliability features. The modular structure and the inherent winding redundancy of dual three-phase machines are noticeable attributes that make these fault-tolerant machines particularly suitable for safety-critical applications. However, conventional thermal networks might produce misleading results, when applied to dual three-phase machines. Indeed, they generally neglect the thermal mutual coupling between windings belonging to different phase sets, since only a single slot is modelled. This paper addresses the aforementioned issue by presenting two lumped parameters thermal networks (second- and third-order), which account for the thermal behavior of both winding sets. The proposed thermal networks are experimentally validated and between them, the third-order one is chosen as best candidate for predicting the windings' temperature, due to its simplicity, accuracy and fast computational time.