In thermal plasma spectroscopy, the Boltzmann plot method is particularly popular for measuring plasma temperature independently of pressure. In order to better understand the results of the Botzmann plot measurements performed with atomic oxygen lines on our thermal plasma, which has a non-negligible thickness, a Python code was developed based on the assumption of local thermodynamic equilibrium (LTE) and the calculated plasma composition and properties. This code allows us to simulate a measurement of the oxygen line intensity resulting from an integration over the plasma thickness in a chosen direction for a given temperature profile. From these a simulated Boltzmann plot gave us a simulated temperature. It resulted that this measurement is governed by the maximum of the temperature profile until the maximum temperature exceeds that of the maximum emissivity of the atomic oxygen lines. Above that temperature a limitation was observed, it is possible to measure higher temperatures but the interpretation of that measurement is difficult. Plasma pressure has a limited effect on this limitation. When no limitation is observed, the temperature measurement from the Boltzmann plot method that we simulated is always at least 90% of the maximum of the temperature profile.