Thermal management of high-power X-ray rotating anodes is strictly constrained by the intense, localized heat fluxes generated during brief exposure times. This study proposes the integration of a lithium-based Rotating Pulsating Heat Pipe (RPHP) into the anode and investigates its transient thermal-hydraulic performance using a Volume of Fluid (VOF) multiphase model, which is heavily influenced by both extreme centrifugal forces and the intense heat flux applied during the exposure time. The results reveal a fundamental thermodynamic trade-off governing the optimal rotational speed: while higher rotational speeds enhance internal fluid circulation as well as latent and sensible heat transport, they simultaneously generate massive hydrostatic pressures that cause a significant transient delay in the phase-change (boiling) process. Consequently, the maximum exposure time exhibits a non-monotonic dependence on the rotational speed. A case study based on the RAD-14 X-ray tube was investigated with a heat input of 20 kW on a minimum focal spot size (0.3 mm). A critical temperature limit of 2200 K was defined to evaluate and compare the allowable exposure times across different configurations. Compared to a conventional solid anode (which is limited to an exposure time of 0.436 s), the RPHP integration at 8500 RPM achieves optimal thermal performance, extending the allowable exposure time to 0.706 s (a 62% increment). However, further increasing the speed to 10000 RPM exacerbates the pressure-induced boiling retardation, leading to an exposure time of 0.619 s (a 42% increment relative to the solid base, but a 12% reduction compared to the 8500 RPM peak).