Computational fluid dynamics is used to simulate the fore-body heating of the free flight experiment (EXPERT project), a ballistic reentry to Earth at 5 km/s. Results are obtained in two different locations of the trajectory. Shortcomings of state-of-the-art models for chemistry and energy exchange terms are briefly discussed. In particular, two different multi-temperature models are compared with the classical two temperature approach proposed by C. Park. An additional computation is performed assuming plain chemical non-equilibrium in order to assess the extent of thermal non equilibrium. The computations are carried out using a parallel implicit high order cell-centered Finite Volume solver implemented within an object oriented framework for multi-physics simulations, currently being developed at the Von Karman Institute. It can handle chemically reacting flows with thermal non equilibrium effects, making use of the multi-temperature approach.