The practical possibilities for solving the inverse problem of complete retrieval of the vertical vibrational temperature profiles for the low-lying vibrational state of the CO₂ molecule were investigated by numerical modeling of satellite measurements of outgoing radiation of the atmosphere in the 15-μm band. Theoretical estimates of the accuracy of the reconstruction of the vibrational-temperature profiles were made for a MIPAS type apparatus. The effect of instrumental spectral resolution and noise on retrieval accuracy was investigated. -Journal summary