A geometric design for a microfluidic chip using numerical simulation is presented. Finite element method was employed in order to design the microchannel configuration for a microfluidic chip array. The effect of geometry on the thermal response at the interface between the microfluidic chips and an integrated system, such as a micro-electronic device, was investigated. Dimensionless design charts, obtained from the parametric models, demonstrated that a compromise between a maximum heat transfer and a minimum interface temperature was achieved with an equilateral triangle cross-section at a microchannel spacing to width ratio of two. The transient response of the microfluidic chip implied that the transient analysis corresponded to the steady state results under different boundary conditions.