  Buffer gas cooling with a $^4$He gas is used to perform laser-absorption
spectroscopy of the $^{12}$C$_2$H$_2$ ($\nu_1+\nu_3$) band at cryogenic
temperatures. Doppler thermometry is first carried out to extract translational
temperatures from the recorded spectra. Then, rotational temperatures down to
20 K are retrieved by fitting the Boltzmann distribution to the relative
intensities of several ro-vibrational lines. The underlying helium-acetylene
collisional physics, relevant for modeling planetary atmospheres, is also
addressed. In particular, the diffusion time of $^{12}$C$_2$H$_2$ in the buffer
cell is measured against the $^4$He flux at two separate translational
temperatures; the observed behavior is then compared with that predicted by a
Monte Carlo simulation, thus providing an estimate for the respective total
elastic cross sections: $\sigma_{el}(100\ {\rm K})=(4\pm1)\cdot 10^{-20}$
m$^{2}$ and $\sigma_{el}(25\ {\rm K})=(7\pm2)\cdot 10^{-20}$ m$^{2}$.
