Modern dry low emissions (DLE) combustors are characterized by highly swirling and expanding flows that makes the convective heat load on the gas side difficult to predict and estimate. A coupled experimental–numerical study of swirling flow inside a DLE annular combustor model is used to determine the distribution of heat transfer on the liner walls. Three different Reynolds numbers are investigated in the range of 210,000–840,000 with a characteristic swirl number of 0.98. The maximum heat transfer coefficient enhancement ratio decreased from 6 to 3.6 as the flow Reynolds number increased from 210,000 to 840,000. This is attributed to a reduction in the normalized turbulent kinetic energy in the impinging shear layer, which is strongly dependent on the swirl number that remains constant at 0.98 for the Reynolds number range investigated. The location of peak heat transfer did not change with the increase in Reynolds number since the flow structures in the combustors did not change with Reynolds number. Results also showed that the heat transfer distributions in the annulus have slightly different characteristics for the concave and convex walls. A modified swirl number accounting for the step expansion ratio is defined to facilitate comparison between the heat transfer characteristics in the annular combustor with previous work in a can combustor. A higher modified swirl number in the annular combustor resulted in higher heat transfer augmentation and a slower decay with Reynolds number.