The steady state forced-convective cooling of a heat sink for a power (~1 kW heat power) semiconductor module with staggered pin-fin combination has been investigated on the basis of computer simulations. A commercial software package ABAQUS is used for the development of the computational model. A self-developed subprogram for the calculation of the local heat transfer coefficient between solid and liquid is used. The effect of the thermal conductivity variation of the sink material, volume flow rate of the cooling liquid, total heat power and inlet cooling liquid temperature has been investigated. Dependencies of the thermal resistances, calculated on the bases of highest and average temperatures of the heating surface as a function of the thermal conductivity of the pin-fin sink material, heat power, liquid volume flow rates, and liquid inlet temperature have been obtained. The impacts of the thermal conductivity of the pin-fin sink material and volume flow rate of the cooling liquid on the thermal resistance of the cooling system are shown.