An electric motor-driven compressor includes a housing assembly comprising a motor housing and a compressor housing mounted thereto. The compressor housing contains a centrifugal compressor wheel that is mounted on a shaft of the motor rotor and also defines an air inlet that leads air into the compressor wheel, and a volute that collects the compressed air. Air bearings rotatably support the shaft. Cooling air passages are defined in the housing assembly for supplying cooling air to the air bearings. A diffuser between the exit of the compressor wheel and the volute serves to diffuse the compressed air. The compressor includes a heat shield formed separately from the compressor housing and the motor housing and disposed between them. The heat shield defines one wall of the diffuser and also cooperates with the housing assembly to define part of the cooling air passages for the cooling air supplied to the bearings.