Rotational temperatures T_rot derived from lines of the same OH band are an important method to study the dynamics and long-term trends in the mesopause region near 87 km. To measure realistic temperatures, the rotational level populations have to be in local thermodynamic equilibrium (LTE). However, this might not be fulfilled, especially at high emission altitudes. In order to quantify possible non-LTE contributions to the OH T_rot as a function of the upper vibrational level v′, we studied a sample of 343 echelle spectra taken with the X-shooter spectrograph at the Very Large Telescope at Cerro Paranal in Chile. These data allowed us to analyse 25 OH bands in each spectrum. Moreover, we could measure lines of O₂b(0-1), which peaks at about 94 to 95 km, and O₂a(0-0) with an emission peak at about 90 km. The latter altitude is reached in the second half of the night after a rise of several km because of the decay of a daytime population of excited O₂. Since the radiative lifetimes for the upper levels of the two O₂ bands are relatively long, the derived T_rot are not significantly affected by non-LTE contributions. These bands are well suited for a comparison with OH if the differences in the emission profiles are corrected. For different sample averages, we made these corrections by using OH emission, O₂a(0-0) emission, and CO₂-based temperature profile data from the multi-channel radiometer SABER on the TIMED satellite. The procedure relies on differences of profile-weighted SABER temperatures. For an O₂a(0-0)-based reference profile at 90 km, we found a good agreement of the O₂ with the SABER-related temperatures, whereas the OH temperatures, especially for the high and even v′, showed significant excesses with a maximum of more than 10 K for v′ = 8. The exact value depends on the selected lines and molecular parameters. We could also find a nocturnal trend towards higher non-LTE effects, particularly for high v′. The amplitude of these variations can be about 2 K or less, which tends to be significantly smaller than the total amount of the non-LTE contributions. The variations revealed may be important for dynamical studies based on T_rot derived from OH bands with high v′.