Recent advances in manufacturing based on sacrificial fiber or template techniques have allowed complex networks of microchannels to be embedded in microvascular composites. In the thermal application of interest, a novel battery packaging scheme for electric vehicles is considered where each battery is surrounded by microvascular composite panels for temperature regulation and structural protection. We use simplified thermal and hydraulics models validated against more complex 3D FLUENT simulations and experiments to obtain the surface temperature distribution of the panel and the pressure drops across the microchannels. We further eliminate the cost and complexity associated with mesh generation by applying the interface-enriched generalized finite element method (IGFEM), which allows a non-conforming mesh to capture the discontinuous temperature gradient across the microchannels. The IGFEM thermal solver is then combined with a gradient-based shape optimization scheme to obtain optimal designs of a set of branched microchannel networks. The design parameters are the channel control points, which define the shape of the network. We use the p-mean as a differentiable objective function in place of the maximum temperature. To obtain accurate gradients with respect to the design parameters efficiently, we perform a sensitivity analysis based on a recently developed adjoint method for IGFEM. Starting from many distinct configurations, we obtain the optimal designs for a wide range of network topologies. We also investigate the effect of the coolant flow rate on the optimal design. (C) 2016 Elsevier Ltd. All rights reserved.