  We present an analysis of the X-ray spectrum of the Local Bubble, obtained by
simultaneously analyzing spectra from two XMM-Newton pointings on and off an
absorbing filament in the Southern galactic hemisphere (b ~ -45 deg). We use
the difference in the Galactic column density in these two directions to deduce
the contributions of the unabsorbed foreground emission due to the Local
Bubble, and the absorbed emission from the Galactic halo and the extragalactic
background. We find the Local Bubble emission is consistent with emission from
a plasma in collisional ionization equilibrium with a temperature $\log T_{LB}
= 6.06^{+0.02}_{-0.04}$ and an emission measure of 0.018 cm^{-6} pc. Our
measured temperature is in good agreement with values obtained from ROSAT
All-Sky Survey data, but is lower than that measured by other recent XMM-Newton
observations of the Local Bubble, which find $\log T_{LB} \approx 6.2$
(although for some of these observations it is possible that the foreground
emission is contaminated by non-Local Bubble emission from Loop I). The higher
temperature observed towards other directions is inconsistent with our data,
when combined with a FUSE measurement of the Galactic halo O VI intensity. This
therefore suggests that the Local Bubble is thermally anisotropic.
  Our data are unable to rule out a non-equilibrium model in which the plasma
is underionized. However, an overionized recombining plasma model, while
observationally acceptable for certain densities and temperatures, generally
gives an implausibly young age for the Local Bubble ($\la 6 \times 10^5$ yr).
