This paper proposes and investigates an analytical method for assessing the risk of potential, irreversible demagnetisation in the PMs of electrical machines, equipped with n-stages, Halbach arrays. The higher risk of demagnetisation, synonymous with Halbach arrays imposes that the method be both load and temperature dependant. In fact, the proposed method studies the magnetic field distribution in the air-gap and PM region, for various operating temperatures and expresses these fields as analytical expressions for the no-load and peak load conditions. The model can cater for Halbach arrays with up to n stages, thus making it a versatile tool that can be utilised for various Halbach configurations. Finite element analysis is used to validate the method.The analytical tool is then used for the design and analysis of a high torque density, outer rotor, traction motor. The motor is for an aerospace application and its operating duty cycle imposes very high, short time, peak load conditions at elevated temperatures, posing an elevated risk of irreversible, PM demagnetisation. The model is used to investigate various Halbach configurations for this application, in order to reduce the demagnetisation risk and also improve the general performance of the machine. The analytical method thus provides a computationally efficient tool that can be used to predict and prevent demagnetisation in Halbach-equipped, electrical machines operating in harsh environments such as the aerospace sector.