The Odin satellite is equipped with millimetre and sub-millimetre receivers for observations of several molecular lines in the middle and upper atmosphere of our planet (~25–100 km, the particular altitude range depending on the species) for studies in dynamics, chemistry, and energy transfer in these regions. The same receivers are also used to observe molecules in outer space, this being the astrophysical share of the project. Among the atmospheric lines that can be observed, we find two corresponding to molecular oxygen (118.75 GHz and 487.25 GHz). These lines can be used for retrievals of the atmospheric temperature vertical profile. In this paper, we describe the radiative-transfer modeling for O₂ in the middle and upper atmosphere that we will use as a basis for the retrieval algorithms. Two different observation modes have been planned for Odin, the three-channel operational mode and a high-resolution mode. The first one will determine the temperature and pressure on an operational basis using the oxygen line at 118.75 GHz, while the latter can be used for measurements of both O₂ lines, during a small fraction of the total available time for aeronomy, aimed at checking the particular details of the radiative transfer near O₂ lines at very high altitudes (>70 km). The Odin temperature measurements are expected to cover the altitude range ~30–90 km. PACS Nos.: 07.57Mj, 94.10Dy, 95.75Rs