  In order to precisely determine temperature and density of molecular gas in
the Large Magellanic Cloud, we made observations of optically thin
$^{13}$CO($J=3-2$) transition by using the ASTE 10m telescope toward 9 peaks
where $^{12}$CO($J=3-2$) clumps were previously detected with the same
telescope. The molecular clumps include those in giant molecular cloud (GMC)
Types I (with no signs of massive star formation), II (with HII regions only),
and III (with HII regions and young star clusters). We detected
$^{13}$CO($J=3-2$) emission toward all the peaks and found that their
intensities are 3 -- 12 times lower than those of $^{12}$CO($J=3-2$). We
determined the intensity ratios of $^{12}$CO($J=3-2$) to $^{13}$CO($J=3-2$),
$R^{12/13}_{3-2}$, and $^{13}$CO($J=3-2$) to $^{13}$CO($J=1-0$),
$R^{13}_{3-2/1-0}$, at 45$\arcsec$ resolution. These ratios were used for
radiative transfer calculations in order to estimate temperature and density of
the clumps. The parameters of these clumps range kinetic temperature
$T\mathrm{_{kin}}$ = 15 -- 200 K, and molecular hydrogen gas density
$n(\mathrm{H_2})$ = 8$\times 10^2$ -- 7$\times 10^3$ cm$^{-3}$. We confirmed
that the higher density clumps show higher kinetic temperature and that the
lower density clumps lower kinetic temperature at a better accuracy than in the
previous work. The kinetic temperature and density increase generally from a
Type I GMC to a Type III GMC. We interpret that this difference reflects an
evolutionary trend of star formation in molecular clumps. The
$R^{13}_{3-2/1-0}$ and kinetic temperature of the clumps are well correlated
with H$\alpha$ flux, suggesting that the heating of molecular gas
$n(\mathrm{H_2})$ = $10^3$ -- $10^4$ cm$^{-3}$ can be explained by stellar FUV
photons.
