  Superthin galaxies are a class of bulgeless, low surface brightness galaxies
with strikingly high values of planar-to-vertical axes ratio $\rm(b/a> 10 -
20)$, possibly indicating the presence of an ultra-cold stellar disc. Using the
multi-component galactic disc model of gravitationally-coupled stars and gas in
the force field of the dark matter halo as well as the stellar dynamical code
AGAMA (Action-based Galaxy Modelling Architecture), we determine the vertical
velocity dispersion of stars and gas as a function of galacto-centric radius
for five superthin galaxies (UGC 7321, IC 5249, FGC 1540, IC2233 and UGC00711)
using observed stellar and atomic hydrogen (HI) scale heights as constraints,
using a Markov Chain Monte Carlo Method. We find that the central vertical
velocity dispersion for the stellar disc in the optical band varies between
$\sigma_{0s}$ $\sim$ $10.2 - 18.4$ $\rm{kms}^{-1}$ and falls off with an
exponential scale length of $2.6$ to $3.2$ $R_{d}$ where $R_{d}$ is the
exponential stellar disc scale length. Interestingly, in the 3.6 $\mu$m, the
same, averaged over the two components of the stellar disc, varies between
$5.9$ to $11.8$ $\rm{kms}^{-1}$, both of which confirm the presence of
"ultra-cold" stellar discs in superthin galaxies. Interestingly, the global
median of the multi-component disc dynamical stability parameter $Q_N$ of our
sample superthins is found to be 5 $\pm$ 1.5, which higher than the global
median value of 2.2 $\pm$ 0.6 for a sample of spiral galaxies.
