This research is focused on the temporal heat flux budgeting on a high-pressure turbine exposed to periodic upstream total flow temperature variations using computational fluid dynamics simulations. A high-pressure turbine vane is exposed to sinusoidal upstream total flow temperature oscillations with peak-to-peak variations around 50K at various frequencies. Transient Unsteady Reynolds Average Navier-Stokes simulations (URANS) are performed, taking advantage of the k-w SST transitional turbulent closure. The transitional kw SST model identifies the transient stagnant conditions' impact on the velocity and temperature boundary layers, considering its influence on turbulent production and dissipation and thermal convection while minimizing the computational burden. The proposed numerical set-up is verified against experimental pressure and heat flux distributions over a high-pressure turbine vane. The evolution of the near wall velocity and thermal profiles are described along the periodic operation, identifying the temporal dynamics governing the heat flux distribution. The velocity and static temperature development are also analyzed based on spectral proper orthogonal decomposition to identify the dominant structures responsible for the transient thermal and momentum response. The temporal characterization of the thermal boundary layer and heat flux distribution over the turbine vane enables the design of more efficient flow control and cooling strategies that mitigate heat loading while minimizing the amount of coolant.