A numerical investigation of 3D fluid flow and heat transfer in a rectangular micro-channel has been carried out using water as a cooling fluid in a silicon substrate. Navier-Stokes and energy equations for laminar flow and conjugate heat transfer are solved using a finite volume solver. Solutions are first carefully validated with available analytical and experimental results; the shape of the micro-channel is then optimized using surrogate methods. Ratios of the width of the micro-channel to the depth and the width of the fin to the depth are selected as design variables. Design points are selected through a four-level full factorial design. A single objective function thermal resistance, formulated using pumping power as a constraint, is optimized. Mass flow rate is adjusted by the constant pumping power constraint. Response surface approximation, kriging, and radial basis neural network methods are applied to construct surrogates and the optimum point is searched by sequential quadratic programming.