  We report a 72 ks XMM-Newton observation of the Be/X-ray pulsar (BeXRP) RX
J0812.4-3114 in quiescence ($L_X \approx 1.6 \times
10^{33}~\mathrm{erg~s^{-1}}$). Intriguingly, we find a two component spectrum,
with a hard power-law ($\Gamma \approx 1.5$) and a soft blackbody-like excess
below $\approx 1~\mathrm{keV}$. The blackbody component is consistent in $kT$
with a prior quiescent Chandra observation reported by Tsygankov et al. and has
an inferred blackbody radius of $\approx 10~\mathrm{km}$, consistent with
emission from the entire neutron star (NS) surface. There is also mild evidence
for an absorption line at $\approx 1~\mathrm{keV}$ and/or $\approx
1.4~\mathrm{keV}$. The hard component shows pulsations at $P \approx
31.908~\mathrm{s}$ (pulsed fraction $0.84 \pm 0.10$), agreeing with the pulse
period seen previously in outbursts, but no pulsations were found in the soft
excess (pulsed fraction $\lesssim 31\%$). We conclude that the pulsed hard
component suggests low-level accretion onto the neutron star poles, while the
soft excess seems to originate from the entire NS surface. We speculate that,
in quiescence, the source switches between a soft thermal-dominated state (when
the propeller effect is at work) and a relatively hard state with low-level
accretion, and use the propeller cutoff to estimate the magnetic field of the
system to be $\lesssim 8.4 \times 10^{11}~\mathrm{G}$. We compare the quiescent
thermal $L_X$ predicted by the standard deep crustal heating model to our
observations and find that RX J0812.4-3114 has a high thermal $L_X$, at or
above the prediction for minimum cooling mechanisms. This suggests that RX
J0812.4-3114 either contains a relatively low-mass NS with minimum cooling, or
that the system may be young enough that the NS has not fully cooled from the
supernova explosion.
