This report describes a method that can calculate transient aerodynamic heating and transient surface temperatures at supersonic and hypersonic speeds. This method can rapidly calculate temperature and heating rate time-histories for complete flight trajectories. Semi-empirical theories are used to calculate laminar and turbulent heat transfer coefficients and a procedure for estimating boundary-layer transition is included. Results from this method are compared with flight data from the X-15 research vehicle, YF-12 airplane, and the Space Shuttle Orbiter. These comparisons show that the calculated values are in good agreement with the measured flight data.