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Aerospace vehicles flying at supersonic and hypersonic speeds are subject to increased wall heating rates caused by viscous friction with the gas environment. This extra heat is commonly referred to as convective aerodynamic heating. In wall-modeled large-eddy simulations, the near-wall region of the flow is not resolved by the computational grid. As a result, the effects of aerodynamic heating need to be modeled using a large-eddy simulation wall model. In this investigation, wall-modeled large-eddy simulations of turbulent high-speed flows are performed to address this issue. In particular, an equilibrium wall model is employed in high-speed turbulent Couette flows subject to different combinations of thermal boundary conditions and grid sizes as well as in transitional hypersonic boundary layers interacting with incident shock waves. Specifically, the wall-modeled large-eddy simulations of the Couette flow configuration demonstrate that the shear-stress and heat-flux predictions made by the wall model show only a small sensitivity to the grid resolution even in the most adverse case where aerodynamic heating prevails near the wall and generates a sharp temperature peak there. Additionally, the simulations indicate that the wall model predicts shear stresses and heat fluxes that are mostly proportional to the near-wall velocity in a manner that resembles an approximate power law. In the wall-modeled large-eddy simulation of hypersonic boundary-layer/shock-wave interaction, the model is tested against direct numerical simulations and experiments. It is shown to correctly capture aerodynamic heating and the overall heat transfer rate around the shock-impingement zone, despite the fact that the adverse pressure gradients in that region may involve nonequilibrium effects.