  Using Suzaku data, we had found a $3.4\sigma$ evidence for the X-ray emitting
warm-hot circumgalactic medium (CGM) in the L$^\star$ galaxy NGC 3221. Here we
present XMM-Newton data and outline an efficient, rigorous and well-defined
method to extract the faint CGM signal. We confirm the CGM detection at
$4\sigma$ significance within 30-200 kpc of the galaxy. We claim with $99.62\%$
confidence that the CGM is extended beyond $150$ kpc. The average temperature
of the CGM is 2.0$^{+0.2}_{-0.3} \times 10^6$ K, but it is not isothermal. We
find suggestive evidence for a declining temperature gradient out to 125 kpc
and for super-virial temperature within 100 kpc. While a super-virial
temperature component has been detected in the Milky Way CGM, this is the first
time a temperature gradient has been observed in the warm-hot CGM of any spiral
galaxy. The emission measure profile is well-fit with either a $\beta-$ model
or a constant density profile. Deeper data are required to constrain the
temperature and density profiles. We also confirm the Suzaku result that the
warm-hot CGM is one of the most massive baryon components of NGC 3221 and can
account for the missing galactic baryons.
