Nadir remote sensing of the night side of Mars is challenging, mainly due to the low signal-to-noise ratio of such observations. We show in a companion paper that the abundance of carbon monoxide (CO) during night can be retrieved from the observations of the Planetary Fourier Spectrometer (PFS). This requires, however, an accurate knowledge of the temperature profile, and especially of the night-time thermal inversions, to properly model the atmospheric emission. While the temperature profile is usually retrieved from the ν2 band of CO2 (centered at 667 ​cm−1), this work shows that, for averaged night-time PFS observations built from a large ensemble of spectra, the temperature profile can be retrieved from the more saturated ν3 band of CO2 (centered at 2349 ​cm−1). We show especially that, due to IFOV (instantaneous field-of-view) size differences and boresight offset between the longwave and shortwave channels of PFS, the temperature profile retrieved from the ν3 band is more consistent with the emission observed in the 1-0 band of CO (centered at 2143 ​cm−1), which is used in the second part paper. We provide a complete characterization of the retrieved temperature profiles in terms of error and vertical sensitivity. Using this, we show that using the ν3 CO2 band allows to properly constrain and characterize the thermal inversions encountered near the surface for most night-time observations. The resulting set of temperature profiles is essential for the retrieval of the night-time CO abundance that is presented in the companion paper. Beyond their usefulness for the night-time CO retrieval, we suggest with a last example that temperature profiles retrieved from the ν3 band of CO2 could be use more generally to study surface thermal inversions encountered at night.