The supersonic outlet conditions from a rotating detonation combustor exhibit fluctuations in temperature and pressure that exceed 200% of their mean level. Such unsteady conditions will induce a large convective heat loading onto a downstream supersonic turbine. Hence, the precise evaluation of the thermal load to the vane and rotor is essential to the design of adequate cooling strategies. In this paper, a numerical framework is proposed to compute the convective heat transfer on two types of supersonic turbines: axial and radial outflow. The fluctuations imposed at the turbine inlet were obtained from a nozzle coupled to a rotating detonation combustor. Both radial and axial turbines were designed and subsequently analyzed with full stage unsteady simulations using an Unsteady Reynolds Averaged Navier–Stokes solver. The inlet boundary conditions to the turbine are based on CFD results from a rotating detonation combustor. The unsteady adiabatic convective heat transfer coefficient was obtained from two simulations performed at a fixed homogeneous wall temperature. The heat flux variation in span-wise and stream-wise direction is analyzed in detail. Budgeting of the unsteady heat flux mechanism was performed to identify the driving contributor of the heat transfer within the turbine and finally both designs are compared.