Heat transfer from an isothermally hot flat surface due to swirling coaxial turbulent jet impingement is investigated numerically. The coaxial jet construction consists of implanting a thin-walled round tube inside a coaxial outer pipe. Two different fluid streams or jets, having different average velocities, flow through the inner tube, and the annular space between the inner tube and the outer pipe. The ratio of the average velocities of the jets, the ratio of the pipe diameters, the jet exit Reynolds number, the strength of the swirl, and the separation distance from the jet exit to the impingement surface are the main parameters for this flow configuration. The effects of the swirl strength on the jet impingement heat transfer at the target surface are investigated by computing the flow and thermal fields for various combinations of the problem parameters. The presented results contain the plots of the flow streamlines, the contours of the temperature, the contours of the swirl velocity, as well as the distribution of the local and average Nusselt number on the impingement surface. It is found that, compared to the single round jet, the coaxial jet produces enhanced and more uniform heat transfer at the heated surface. The jet-spreading and mixing are affected by the imposed jet swirl which modifies the heat transfer process. Thus, the heat transfer compared to a non-swirling jet is either enhanced or diminished depending on the combination of the problem parameters.