The objective of this study is to develop a reliable and efficient design optimization method for hypersonic vehicles focused on aerothermodynamics. Considering the nature of hypersonic flight, a high-fidelity aerothermodynamic analysis code is utilized for the simulation of weakly ionized hypersonic flows in thermo-chemical non-equilibrium. A gradient-based method is implemented for optimization. Bezier or NURBS curves are used to parametrize the geometry or the geometry change. Linear elasticity theory is implemented for mesh deformation. Penalty functions are utilized to prevent undesired geometrical changes. The design objective is to minimize drag without increasing the heat transfer rate and the maximum values of the surface heat flux, temperature and pressure. Design optimizations are performed at different trajectory points of the IRV-2 vehicle. The effects of parametrizations, the number of design variables and freestream conditions on design performance are studied.