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We explore a novel method for measuring the average temperature of the$\nu_x$ component in Type-II core-collapse supernovae. By measuring neutralcurrent incoherent neutrino-Argon interactions in DUNE we can obtain spectralinformation for the combination of all active neutrino species. Combining thisall-neutrino spectral information with detailed charged current measurements ofthe electron neutrino and electron anti-neutrino fluxes from DUNE andHyper-Kamiokande, we can infer the average temperature for the remainingneutrino species in the $\nu_x$ component to within a factor two for most casesand to 30% for a small range of average $\nu_x$ temperatures. Due to thelimited energy range of the emitted photons from incoherent neutral currentinteractions on Argon, the $\nu_x$ temperature reconstruction demonstrates adegeneracy in the one and two sigma credible regions. Furthermore, while largeuncertainties on the NC cross-section penalize this measurement, we examinedthe efficacy of constraining NC cross-section uncertainties on improving$\nu_x$ measurements. We found that if additional measurements ofB(M1$\uparrow$) 1$^+$ excited state transitions in Argon are able to reducecorrelated cross section uncertainties from 15% to 7%, the size of the$1\sigma$ allowed regions for $T_{\nu_x}$ becomes sample size limited, andapproaches the case where there are no uncertainties on the cross-section.

Sensitivity to Supernovae Average $\nu_x$ Temperature with Neutral Current Interactions in DUNE