In this paper we consider the complete thermofluid design and performance of a thermoelectric module. We increase the temperature difference that must be maintained across the module, and at the same time we reduce the pumping power required by the streams that bathe the hot and cold plates of the module. We find that for greater power output the two streams must be configured in parallel, not in counterflow, and not between two well mixed plenums. We also find that the loss of thermoelectric power due to the temperature nonuniformity of the two plates competes with the power lost during the pumping of the two streams, and that from this competition results the optimal mass flow rates of the two streams. At the optimum, the maximized power output of the module is proportional to a group of geometric parameters (Eq. (39)), which can be maximized further by designing vascular flow architectures for the two plates. The vascular designs reveal an optimal ratio of channel diameters, optimal plate aspect ratio, and a channel flow volume fraction that is of the same order as the ratio of the fluid thermal conductivity divided by the solid thermal conductivity. The flow architectures are further illustrated with numerical examples of vascular and serpentine configuration and performance. (C) 2014 Elsevier Ltd. All rights reserved.