An electrically heated aerosol-generating device is configured for use with a consumable cartridge including a storage portion containing an aerosol-forming substrate and having a fluid permeable internal surface surrounding an open-ended passage extending through the cartridge. The device includes a housing having a cavity for receiving the cartridge and a heater assembly positioned in the cavity. The heater assembly includes an electrically conductive hollow shaft portion connected to the housing and an electric heater positioned along the hollow shaft portion and having at least one heating element for heating the aerosol-forming substrate. The hollow shaft portion defines an airflow passage forming part of an airflow pathway through the device and is arranged to extend into the open-ended passage of the cartridge. The hollow shaft portion comprises a plurality of apertures, and the heating element is one or more narrow regions of the hollow shaft portion between adjacent apertures.