Rotating Detonation Combustors (RDC) offer a very high-power density compared to other combustors. Although they must overcome many challenges to be integrated into a gas turbine (GT), it is certainly a promising solution for increasing cycle efficiency. Among the many challenges, cooling the RDC is one of the most predominant, due to the high heat loads generated by the combustion process. Most of the available numerical and experimental data in the literature about RDC heat loads are obtained for laboratory conditions (i.e. at atmospheric pressure). However, in order to design a cooling system for an RDC that allows for its sustainable operation and aids its integration to GT engines, a quantification of the heat loads of an RDC with GT conditions is necessary. The presence of a detonation wave/boundary layer interaction and a small annulus width leads to a very high heat transfer when compared to a conventional GT combustor.