Single-laser-shot temperature measurements at 5kHz were performed in a model gas turbine combustor using femtosecond (fs) coherent anti-Stokes Raman scattering (CARS). The combustor was operated at a global equivalence ratio of 0.65 and 10kW thermal power. Measurements were performed at various locations within the flame in order to resolve the spatial flame structure and compare to previously published studies. Power spectral density analysis of the temperature measurements yielded the characteristic thermo-acoustic pulsation frequency previously reported at 308Hz. These results demonstrate the usefulness of fs-CARS for the investigation of highly turbulent combustion phenomena. The spatial resolution of the single-laser shot temperature measurements was approximately 600μm, the precision was approximately ±2%, and the estimated accuracy was approximately ±3%. The dynamic range was sufficient for temperature measurements ranging from 300K to 2400K, although some detector saturation was observed for low temperature spectra.