With the purpose of assessing classic spectroscopic methods on high-resolution and high signal-to-noise ratio spectra in the near-infrared wavelength region, we selected a sample of 65 F-, G-, and K-type stars observed with CARMENES, the new, ultra-stable, double-channel spectrograph at the 3.5 m Calar Alto telescope. We computed their stellar atmospheric parameters ($T_{rm eff}$, $log{g}$, $xi$, and [Fe/H]) by means of the StePar code, a Python implementation of the equivalent width method that employs the 2017 version of the MOOG code and a grid of MARCS model atmospheres. We compiled four Fe I and Fe II line lists suited to metal-rich dwarfs, metal-poor dwarfs, metal-rich giants, and metal-poor giants that cover the wavelength range from 5300 to 17100 angstroms, thus substantially increasing the number of identified Fe I and Fe II lines up to 653 and 23, respectively. We examined the impact of the near-infrared Fe I and Fe II lines upon our parameter determinations after an exhaustive literature search, placing special emphasis on the 14 $Gaia$ benchmark stars contained in our sample. Even though our parameter determinations remain in good agreement with the literature values, the increase in the number of Fe I and Fe II lines when the near-infrared region is taken into account reveals a deeper $T_{rm eff}$ scale that might stem from a higher sensitivity of the near-infrared lines to $T_{rm eff}$.
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