A solid-oxide fuel cell system having a relatively large primary fuel cell sub-assembly for steady-state operation and a relatively small secondary fuel cell sub-assembly which is rapidly heatable to a threshold operating temperature to a) produce usable power in a short time period, b) cascade a hot exhaust into the primary fuel cell sub-assembly to assist in preheating thereof, and c) provide steam into the primary fuel cell sub-assembly to prevent coking of the anodes thereof. As the primary sub-assembly reaches its threshold temperature, it too begins to generate electricity and continues to self-heat and to be heated by the secondary sub-assembly. Preferably, the secondary sub-assembly continues to provide electricity in complement with the primary sub-assembly until the primary sub-assembly reaches full power, at which time the secondary sub-assembly may be shut down or switched to standby status for fuel efficiency, as desired.