Vibrational relaxation of a single-component carbon dioxide in adiabatic thermal bath is studied in multi-temperature approaches using several models for the vibrational relaxation time. The energy production terms in two- A nd three-temperature vibrational energy relaxation equations are written in the frame of the common Landau-Teller model as well using corrections based on introducing multi-temperature relaxation times for various vibrational energy exchanges within and between CO2 modes. For the relaxation time evaluation, two theoretical models for the transition probabilities are implemented: The first-order perturbation theory and the forced harmonic oscillator model; several experimental data sets are also assessed. It is shown that the forced harmonic oscillator model provides satisfactory agreement with experimental relaxation times in a wide temperature range. Solutions obtained using the two theoretical models for the transition probabilities show essentially different trends, incubation time and relaxation rate.