Characterizing Earth- and Venus-like exoplanets' atmospheres to determine if they are habitable and how they are evolving (e.g., equilibrium or strong erosion) is a challenge. For that endeavor, a key element is the retrieval of the exospheric temperature, which is a marker of some of the processes occurring in the lower layers and controls a large part of the atmospheric escape. We describe a method to determine the exospheric temperature of an O2- and/or CO2-rich transiting exoplanet, and we simulate the respective spectra of such a planet in hydrostatic equilibrium and hydrodynamic escape. The observation of hydrodynamically escaping atmospheres in young planets may help constrain and improve our understanding of the evolution of the solar system's terrestrial planets' atmospheres. We use the dependency of the absorption spectra of the O2 and CO2 molecules on the temperature to estimate the temperature independently of the total absorption of the planet. Combining two observables (two parts of the UV spectra that have a different temperature dependency) with the model, we are able to determine the thermospheric density profile and temperature. If the slope of the density profile is inconsistent with the temperature, then we infer the hydrodynamic escape. We address the question of the possible biases in the application of the method to future observations, and we show that the flare activity should be cautiously monitored to avoid large biases.