Measurements of the Doppler width of the 6300 {\AA} airglow emission
line have been extensively used to determine the thermospheric
temperature. This technique is based on the assumption that the bulk
of the emitting O($^1$D) atoms are thermalized in the region of the
airglow source (200-300 km). A Monte Carlo stochastic model is used to
calculate the energy distribution function of O($^1$D) atoms in the
dayand nighttime thermosphere. Hot O($^1$D) atoms are produced by
exothermic processes and their thermalization is controlled by the
competition between radiation, collisional quenching and relaxation.
It is found that the O($^1$D) temperature departs from the background
gas temperature not only in the upper thermosphere but also in the
region of the bulk 6300 {\AA} emission. At 300 km, for low solar
activity conditions, the model predicts an excess O($^1$D) temperature
of $\sim$ 180 K during daytime and $\sim$ 950 K at night. The
temperature departure persists at lower altitudes as a result of the
major contribution of the O$_2^+$ dissociative recombination source of
hot $^1$D atoms. Experimental evidence based on the Fabry-Perot
interferometer measurements on board the Dynamics Explorer satellite
confirms the existence of an O($^1$D) temperature excess over the MSIS
value. It is concluded that temperatures deduced from the 6300 {\AA}
airglow line width exceed the ambient gas temperature by an amount
which may be significant.