Buffer gas cooling with a $^4$He gas is used to perform laser-absorption spectroscopy of the $^{12}$C$_2$H$_2$ ($ u_1+ u_3$) band at cryogenic temperatures. Doppler thermometry is first carried out to extract translational temperatures from the recor
ded 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: $sigma_{el}(100 {rm K})=(4pm1)cdot 10^{-20}$ m$^{2}$ and $sigma_{el}(25 {rm K})=(7pm2)cdot 10^{-20}$ m$^{2}$.
