The aerothermal design of vehicles operating in the hypersonic regime, such as re-entry capsules, relies on the accurate prediction of the flow field and of the loads and heat fluxes on their surface. In this regime a strong bow shock compresses the gas to very high temperatures, activating thermochemical processes such as vibrational excitation, dissociation and ionization, where the hypothesis of thermal and chemical equilibrium does not apply and require stiff, coupled multi-species, multi-temperature models. Explicit schemes are inefficient, as their stability limit imposes small time steps to advance the solution, requiring long periods of time to achieve convergence. Implicit schemes are free from this constraint and accelerate the convergence to steady state, at the cost of solving a large sparse linear system at each iteration..