Heat and mass transfer in a planar anode-supported solid oxide fuel cell (SOFC) module, with bipolar-plate interconnect flow channels of different shapes are computationally simulated. The electrochemistry is modeled by uniform supply of volatile species (moist hydrogen) and oxidant (air) to the electrolyte surface with constant reaction rate via interconnect channels of rectangular, trapezoidal, and triangular cross sections. The governing three-dimensional equations for fluid mass, momentum, energy, and species transport, along with those for electrochemical kinetics, where the homogeneous porous-layer flow is in thermal equilibrium with the solid matrix, are coupled with the electrochemical reaction rate to properly account for the heat and mass transfer across flow-ducts and electrode-interfaces. The results highlight effects of interconnect duct shapes on lateral temperature and species distributions as well as the attendant frictional losses and heat transfer coefficients. It is seen that a relatively shallow rectangular duct offers better heat and mass transfer performance to affect improved thermal management of a planar SOFC.