In recent years, researchers are investigating several potential applications of two-phase flow in micro-gap heat sinks; electronic cooling is one of them. Further, internal micro-fins are used to enhance the heat transfer rate. However, the pressure drop penalty due to small gap height and fin surfaces is a major concern. Hence, minimization of thermal resistance and pressure drop is required. In this paper, effects of operating conditions, e.g., wall heat flux, pumping power, and inlet void fraction, on total thermal resistance and pressure drop in a micro-gap heat sink with internal micro-fins of rectangular and triangular profiles have been investigated by numerical analysis for the R-134a coolant. Furthermore, optimization of these parameters has been carried out by response surface methodology. Simulation results show that rectangular micro-fins show superior performance compared to triangular fins in reducing thermal resistance. Finally, for an optimum condition (7.1202×10-5 W pumping power, 1.2×107 Wm-2 heat flux, and 0.03 inlet void fraction), thermal resistance and pressure drop are reduced by 56.3% and 87.2%, respectively.