The power of the air to deliver heat to a surface should go something not a huge distance away from density times speed-cubed per unit area. Close to shocks you might need to be careful, but that's the power there is in the flow.
When shockwaves form it gets more complicated, and the nature of the associated upstream changes in speed, density and temperature can be important.
The efficiency of cooling also affects the final surface temperature, so the surface and structural properties affect the answer too. Key components of short-lived items can cope if handled with conductive, ablative or radiative cooling.