  NGC 362 is a non-common Type II Galactic globular cluster, showing a complex
pseudo two-color diagram or 'chromosome map'. The clear separation of its
stellar populations in the color-magnitude diagram and the distribution of the
giant stars in the chromosome map strongly suggests that NGC 362 could host
stars with both cluster-nominal as well as enhanced heavy-element abundances,
and one of them could be iron. However, despite previous spectroscopic
observations of NGC 362, no such iron variation has been detected. Our main
goal is to confirm or disprove this result by searching for any internal
variation of [Fe/H] which would give us insight into the formation and
evolution of this interesting globular cluster. In this paper, we present the
abundance analysis for a sample of 11 red giant branch members based on
high-resolution and high S/N spectra obtained with the MIKE echelle
spectrograph mounted at the Magellan-Clay telescope. HST and GAIA photometry
and astrometry has been used to determine atmospheric parameters and
membership. We obtained T$_{\text{eff}}$, log(g) and v$_{\text{t}}$ for our
target stars and measured the mean iron content of the sample and its
dispersion with three different methods, which lead to
[Fe/H]$_1$=-1.10$\pm0.02$, [Fe/H]$_2$=-1.09$\pm0.01$ and
[Fe/H]$_3$=-1.10$\pm0.01$, while the internal dispersion turned out to be
$\sigma_{[\text{Fe/H}]_1}$=0.06$\pm0.01$,
$\sigma_{[\text{Fe/H}]_2}$=0.03$\pm0.01$ and
$\sigma_{[\text{Fe/H}]_3}$=0.05$\pm0.01$ respectively. The error analysis gives
an internal dispersion due to observational error of 0.05 dex. Comparing the
observed dispersion with the internal errors, we conclude that NGC 362 does not
show any trace of an internal iron spread.
