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A thermal analysis of three different rotor constructions for a high-speed permanent-magnet electrical machine is performed. The first type of rotor has a carbon-fibre sleeve for retaining the magnets against the centrifugal forces and an aluminium shield for eddy currents. The other two rotors have retaining sleeves made of different titanium alloys and do not have additional eddy-current shields. The thermal analysis of the rotor types is performed using two completely different approaches. The first implemented method is a numerical-multiphysics one that couples computational fluid dynamics equations with heat-transfer equations. For better reliability of the analysis, a traditional thermal-network method is also implemented for estimation of the temperature distribution in the examined rotors. The accuracy of the aforementioned methods is verified using experimental results for the average temperature rise of the permanent magnets. The results obtained from the implemented methods show that although the rotor with a retaining sleeve made of titanium alloy Ti-6%Al-6%V-2%Sn does not have any eddy-current shield, it fulfils the thermal constraints and can be implemented for high-speed applications.