We present coordinated coronal observations of the August 21, 2017 total solar eclipse with the Airborne Infrared Spectrometer (AIR-Spec) and the Extreme-ultraviolet Imaging Spectrometer (EIS). These instruments provide an unprecedented view of the solar corona in two disparate wavelength regimes, the near to mid infrared (IR) and the extreme ultraviolet (EUV), opening new pathways for characterizing the complex coronal plasma environment. During totality, AIR-Spec sampled coronal IR spectra near the equatorial west limb, detecting strong sources of Mg VIII, S XI, Si IX, and Si X in two passbands encompassing 1.4 - 4 $mu$m. We apply emission measure (EM) loci analysis to these IR emission lines to test their capacity as coronal temperature diagnostics. The density-sensitive Fe XII 186.9 r{A}/192.4 r{A} line pair supplies spatially resolved, line-of-sight electron densities, supporting the EM loci analysis. From this, we find EM loci intersections at temperatures of $10^{6.13}$ K at 30 arcsec from the limb and $10^{6.21}$ K at 100 arcsec. Applying the same EM loci analysis to 27 EIS emission lines associated with seven ion species (Fe X-XIV, S X, and Si X) confirms these results, displaying strong evidence of isothermal plasma throughout the region. However, the IR EM loci analysis suffers from moderate uncertainties. The likely sources include: poor signal, infrared contamination from a prominence, and photoexcitation by continuum radiation. Regardless, we demonstrate that EUV spectral data are valuable constraints to coronal infrared emission models, and will be powerful supplements for future IR solar observatories, particularly DKIST.
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