We have computed altitude profiles for O+ ion temperature partition coefficients ¿$parallel$ and ¿$perp$ in the auroral ionosphere for different values of electric field with the use of a Monte Carlo simulation. The Monte Carlo model includes the effect of E ¿ B drift, O+--O (resonant charge exchange and polarization interaction) collisions, and O+--O+ Coulomb self-collisions. These effects were included self-consistently in the computations. At low altitudes, the O+ ion concentration is small compared with the O concentration; thus the role of O+--O+ Coulomb self-collisions in isotropizing the O+ ion velocity distribution is negligible and hence non-Maxwellian features (¿$perp$ > ¿$parallel$) are obtained due to the effect of O+--O collisions. However, as altitude increases, the O+ concentration increases and consequently, the role of O+--O+ Coulomb collisions becomes significant in transferring energy from the field-perpendicular direction to the field-parallel direction. This explains the increase of ¿$parallel$ and the decrease of ¿$perp$ with altitude. Also, we have investigated the variation of ¿$parallel$ and ¿$perp$ with the electric field and found that as electric field increases, O+ ion temperature increases, ¿$parallel$ decreases, and ¿$perp$ increases due to the interplay between E ¿ B drift and O+--O collisions. In other words, the effect of O+--O+ Coulomb collisions becomes less important because these Coulomb collisions are in turn dependent on O+ ion temperature. Therefore the combined effects of E ¿ B drift, O+--O collisions, and O+--O+ Coulomb collisions determine the altitude profiles of ¿$parallel$ and ¿$perp$. Finally, a comparison has been made between the Monte Carlo calculations obtained in this paper and observations of the O+ ion temperature partition coefficient ¿$parallel$. The comparison showed a remarkably close agreement in the corresponding results for the altitude variation of ¿$parallel$. This close agreement provides further evidence that the Monte Carlo model described in this paper is a powerful tool for studying O+ ion behavior in the auroral ionosphere, especially when O+--O+ Coulomb self-collisions are included. As a result of the comparison, we were able to predict the real values of the convection electric field in the auroral ionosphere for three ion heating events.