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Context. Detailed characterizations of exoplanets are moving to the forefrontof planetary science. Temperature is a key marker for understanding atmosphericphysics and chemistry. Aims. We aim to retrieve temperatures of N2-O2 dominatedatmospheres from secondary eclipse spectroscopic observations of the thermalemission of Earth-like exoplanets orbiting G-, K-, and M-stars using largefuture space telescopes. Methods. Line-by-line radiative transfer was used togenerate synthetic thermal infrared (TIR) observations. Atmospheric temperatureis approximated by an expansion with base vectors defined by a singular valuedecomposition of a matrix comprising representative profiles. Nonlinear leastsquares fitting is used to estimate the expansion coefficients. Results.Analysis of the $4.3 \rm\,\mu m$ and $15 \rm\,\mu m$ CO2 bands in the TIRpermits inference of temperatures even for low signal-to-noise (S/N) ~5 atmedium resolution. Deviations from the true temperature in the uppertroposphere and stratosphere are usually a few Kelvin, with larger deviationsin the upper atmosphere and, less often, in the lower troposphere. Although theperformance of the two bands is equivalent in most cases, the longwave TIR ismore favorable than the shortwave due to increased star-planet contrast. A highspectral resolution, as provided by JWST instruments, is important forretaining sensitivity to the upper atmosphere. Furthermore, the selection of anappropriate set of base functions is also key. Conclusions. Temperature in themid-atmosphere can be suitably characterized by IR spectroscopy with aresolution of at least 1000 (ideally ~2500). Obtaining the necessary S/N couldbe feasible with future missions, such as the Origins Space Telescope or theLarge Interferometer for Exoplanets. Meanwhile a least squares fitting withappropriate base functions is also applicable for other classes of planets.

SVEEEETIES: Singular vector expansion to estimate Earth-like exoplanet temperatures from infrared emission spectra