The use of tetrahedral, prismatic, and hybrid hexahedral-prismatic- tetrahedral grids for the accurate prediction of aerodynamic heating at hypersonic conditions is investigated. We find that tetrahedral grids introduce significant error in the vicinity of strong shock waves, which results in unacceptable aeroheating predictions. The source of this error is studied with an idealized model, and it is found that a large spurious component of post-shock velocity is generated by triangular and tetrahedral elements. This type error is much smaller and easier to control on quadrilateral or hexahedral grids. Thus, we are very skeptical about the utility of tetrahedral grids for accurate hypersonic aeroheating predictions. Several comparisons of heating predictions for a three-dimensional sphere are made, and it is found that the stagnation region results are very sensitive to the grid design. Based on this work and our experience, we advocate the use of unstructured hexahedral grids which increase the grid design space, reduce the element count for many geometries, and result in accurate aeroheating predictions.