Numerical calculations of heat transfer characteristics of an impingement cooling system with a non-uniform temperature on a cooled surface using ANSYS CFX have been performed. The influence of a surface heat flux qw(x) and a nozzle shape on the Nusselt number distribution on the cooled surface has been studied. The setup consisted of a cylindrical plenum with an inline array of ten impingement jets. Cylindrical, convergent divergent shapes of nozzles and linear temperature distribution on the cooled surface have been considered for various heat fluxes qw(x). Results indicate that geometry of the cylindrical nozzles resulted in the highest Nusselt numbers along the cooled surface. The line of the averaged Nusselt number has a trend to increase in the direction of the flow for the cooling system with increasing values of the surface heat flux q(x). This tendency can be observed for all presented shapes of jets. On the other hand, for decreasing functions of the heat flux qw(x), the Nusselt number distribution is more uniform. It can be observed for all types of nozzles. Very similar values of the Nusselt number occur especially for the non-uniform heat flux 5000-2500W/m2. For constant values of the heat flux q(x) = 5000W/m2, the line of the average Nusselt number has a trend to increase slightly in the direction of the flow. Numerical analysis of different mesh density results in good convergence of the GCI index, what excludes mesh size dependency. The presented study is an extension of the paper (Marzec and Kucaba-Piętal, 2016) and aims at answering the question how the Nusselt number distribution on the cooled surface is affected by various geometries of nozzles for a non-uniform surface heat flux qw(x).