An unsteady simulation of a two-stage, cooled, high pressure turbine cascade is achieved by applying the harmonic balance method, a mixed time domain and frequency domain computational fluid dynamic technique for efficiently solving periodic unsteady flows. A comparison of computed temperature and pressure profile predictions generated using the harmonic balance method and a conventional steady mixing plane analysis is presented. The predicted temperature and pressure profiles are also compared to experimental data at the stage exit plane. The harmonic balance solver is able to efficiently model unsteady flows caused by wake interaction and secondary flow effects due to cooling flows. It is demonstrated that modeling the unsteady effects is critical to the accurate prediction of time-averaged flow field quantities, particularly for cooled machines.