  133P/Elst-Pizarro is the firstly recognized main-belt comet, but we still
know little about its nucleus. Firstly we use mid-infrared data of
Spitzer-MIPS, Spitzer-IRS and WISE to estimate its effective diameter $D_{\rm
eff}=3.9^{+0.4}_{-0.3}$ km, geometric albedo $p_{\rm v}=0.074\pm0.013$ and mean
Bond albedo $A_{\rm eff,B}=0.024\pm0.004$. The albedo is used to compute 133P's
temperature distribution, which shows significant seasonal variation,
especially polar regions, ranging from $\sim40$ to $\sim200$ K. Based on
current activity observations, the maximum water gas production rate is
estimated to be $\sim1.4\times10^{23}\rm~s^{-1}$, being far weaker than
$\sim10^{26}\rm~s^{-1}$ of JFC 67P at similar helio-centric distance $\sim2.7$
AU, indicating a thick dust mantle on the surface to lower down the gas
production rate. The diameter of the sublimation area may be $<\sim200$ m
according to our model prediction. We thus propose that 133P's activity is more
likely to be caused by sublimation of regional near-surface ice patch rather
than homogeneous buried ice layer. Such small near-surface ice patch might be
exposed by one impact event, before which 133P may be an extinct comet (or
ice-rich asteroid) with ice layer buried below $\sim$40 m depth. The proposed
ice patch may be located somewhere within latitude $-50\sim50^\circ$ by
comparing theoretical variation of sublimation temperature to the constraints
from observations. The time scale to form such a thick dust mantle is estimated
to be $>100$ Myr, indicating that 133P may be more likely to be a relatively
old planetesimals or a member of an old family than a recently formed fragment
of some young family.
