Concentrated windings are favourable in electric motors with a high torque density because of the achievable high winding filling factor and their short end-windings. Nevertheless, the performance of the cooling system has the biggest impact on the reachable torque density limits. This article introduces a thermally conductive insert piece that encloses the stator end-windings with extensions in the stator slots. This results in an extended contact surface between the stator windings and the machine housing, which is advantageous for the conductive heat transfer. The introduced indirect cooling concept is compatible with traditional cooling techniques such as forced air and water jacket cooling. The concept is illustrated with 3D thermal finite element simulations, including the anisotropic thermal material properties, as well as ad hoc measurements on a stator pole unit mock-up of a 6-4 switched reluctance machine. Where the stator with reference cooling system was only able to handle a continuous current density of 19.0 A/mm $^2$ , 26.5 A/mm $^2$ could be obtained in the winding of the stator with the extended end-winding cooling inserts.