Liquid cooling with water-glycol mixtures is the prevailing method for cooling electric machines due to its efficiency and cost-effectiveness. However, there is ongoing research on using liquid metal as a cooling fluid for low-temperature applications which remains largely unexplored. The eutectic mixture GaInSn (7%Ga, 20.5% In, and 12.5% Sn by volume) is gaining popularity as a cooling fluid due to its favourable properties, such as easy handling, excellent thermal characteristics, compatibility with common materials, and low melting point. This study examines the feasibility of using liquid metal in stator windings with integrated cooling channels, focusing on the thermal benefits through computational fluid dynamics (CFD) analysis. A comparison is made between a machine design with integrated cooling using alternative liquid coolants, and a baseline design that relies on the conventional water-glycol 'jacket' type cooling of the motor housing. The initial theoretical findings indicate that liquid metal offers a distinct thermal performance advantages over conventional cooling solutions. However, there are still compatibility issues, including thermal, mechanical, and electromagnetic considerations, that need to be addressed to fully exploit the potential of this approach.