Improving the efficiency of gas turbines is of paramount importance. One promising approach is the implementation of Pressure Gain Combustion (PGC) technologies, among which the Rotating Detonation Combustor (RDC) has attracted significant attention. However, numerous challenges impede its integration into gas turbines, and the thermal management of the combustor liner represents one of the most relevant. This liner is subjected to thermal loads far exceeding those in conventional gas turbines. This thesis investigates the mechanisms driving thermal loads in RDCs and explores strategies to mitigate them. Results indicate that thermal loads are primarily driven by the increased frequency of rotating detonations within the combustor. Numerical and experimental analyses reveal highly variable thermal loads, with both temperature and heat transfer coefficients influenced by numerous design parameters and operating conditions. To address these uncertainties, a fast evaluation tool was developed to assess the compatibility of prescribed thermal loads with generalized forced convection cooling systems. The findings indicate that the cooling requirements for such systems are often impractically high, rendering convection-based approaches inefficient for RDCs. To overcome this limitation, the thesis evaluates the feasibility of film cooling in RDCs. Given the extensive regions of supersonic flow in RDCs and the limited research on film cooling under such conditions, an experimental study was conducted. A test rig capable of generating a Mach 1.65 flow to a film-cooled test section was designed and built. Two experimental techniques were employed: schlieren imaging to observe shock wave formation caused by coolant injection, and pressure sensitive paint (PSP) to measure pressure distribution and adiabatic effectiveness, a key metric for film cooling performance. Results show that coolant injection generates oblique shock waves upstream of the cooling holes, which help retain the coolant near the surface. Adiabatic effectiveness measurements reveal superior cooling performance in supersonic flows compared to subsonic conditions. For cylindrical cooling holes, the improvement is noticeable just a few diameters downstream of the holes, regardless of the blowing ratio. For fan-shaped holes, the onset of superior performance occurs 10–15 diameters downstream at low blowing ratios but spans the entire domain at higher blowing ratios. This study provides a complete description of film cooling in supersonic flows, considering both flowfield morphology and performance for different operating conditions and 3 different cooling hole geometries. It is the first study to use PSP techniques to evaluate adiabatic effectiveness in a supersonic main flow, eliminating errors associated with thermal-based approaches. The findings suggest that film cooling is a viable strategy for managing thermal loads in RDCs and other components exposed to supersonic flows. This work lays the foundation for more sustainable gas turbine designs employing RDC technology.