An analysis is made of the influence of finite electrical conductivity of the walls on fully developed magnetohydrodynamic channel-flow heat transfer. The analysis is based on arbitrary external electrical loading and is thus valid for both generator and accelerator modes of operation. Constant properties of the fluid and walls are assumed. It is shown that under certain operating conditions of external electrical loading, the fluid bulk to wall temperature difference for conducting walls differs substantially from that for electrically insulating walls. Representative numerical calculations are presented.