The ability to predict surface heating rates, as well as shear and pressure forces, is fundamental to the analysis and design of the thermal protection system for hypersonic vehicles. Approximate engineering codes that can be used to rapidly predict heating rates are extremely useful in the preliminary or conceptual design phase, whereas more detailed and expensive Navier–Stokes codes are generally used to provide more accurate heating rate predictions for final design. An earlier code has been used successfully in conjunction with inviscid flowfield codes computed on single-block structured grids. More recent inviscid codes have been developed that use unstructured grids, which greatly reduce grid generation time for complex configurations. A newer heating code had been used successfully with unstructured inviscid flowfield codes to compute laminar heating on general three-dimensional vehicles using unstructured grids and the heating rates over most of the vehicle have been shown to compare favorably with results from both boundary-layer and Navier–Stokes calculations. However, some anomalies were encountered in the stagnation region. This paper describes the newest version of the approximate heating code, which provides much better heating results in the stagnation region. The new code includes the capability to calculate both laminar and turbulent heating rates, for either perfect gas or equilibrium-air chemistry, with radiation-equilibrium or constant wall temperature boundary conditions. An approximate expression is implemented to account for the effect of velocity gradient on laminar heating. In addition, a new approximate method for computing the effect of finite wall catalysis on surface heating is included. A new improved axisymmetric analog method is developed to calculate inviscid surface streamlines and metric coefficients based on unstructured grids. Results are calculated and compared with both boundary-layer and Navier–Stokes solutions for a range of typical hypersonic vehicles. The new code is directed toward the development of more efficient and accurate approximate engineering methods for predicting heating on hypersonic vehicles and to better understand how these methods can be integrated with more detailed Navier–Stokes results to improve the overall vehicle and thermal design processes.