This paper presents a computational fluid dynamics conjugate heat transfer analysis of internal and external cooling paths for a hollow high-speed permanent magnet rotor. Extracting magnet losses from high-speed permanent magnet rotors is challenging, due to the thermal limits of magnets and composite magnet retention sleeves. This paper proposes the use of internal and external air-cooling paths through the hollow rotor and airgap, respectively. Component temperatures with respect to these cooling paths are investigated. The balance of interactions between the internal, external and component temperatures is complex and is best solved using computational fluid dynamics. The passing of cooling air through and outside the rotor improves the cooling of components. However, there are limits, as forcing progressively more air through the airgap is shown to eventually cause a net heating of the rotor, due to fluid viscous heating effects. Differences in modelling temperature dependent fluid properties is explored and shown to make an important difference when designing machines to maximize their material thermal capabilities.