This paper presents a design of a short term duty electrical machine working in an extreme environment consisting of 80°C ambient temperature and altitudes of over 30,000m. Higher power density is a key factor in the design wherein the machine's operation is required only for a short duty. The requirement of high power-to-weight and power-to-volume leads to a Permanent Magnet (PM) machine design, which is then optimized. Different slot and pole combinations, with both concentrated and distributed winding arrangements are considered. For the optimization, a Genetic Algorithm (GA) is used where analytical electromagnetic and thermal models are adopted together with Finite Element (FE) methods. It is shown that the adopted thermal model provides sufficient accuracy when predicting temperature rise within the winding. It is also shown that the designs are thermally limited where the pole numbers are limited by volt-amps drawn from the converter. The design consisting of a high slot number allows for improving the heat dissipation from the machine and thus, the weight can be minimized for the given torque production.