We demonstrate cryogenic buffer-gas cooling of gas-phase methyltrioxorhenium (MTO). This molecule is closely related to chiral organometallic molecules where the parity-violating energy differences between enantiomers may be measurable. The molecules are produced with a rotational temperature of approximately 6~K by laser ablation of an MTO pellet inside a cryogenic helium buffer gas cell. Facilitated by the low temperature, we demonstrate absorption spectroscopy of the 10.2~$\mu$m antisymmetric Re=O stretching mode of MTO with a resolution of 8~MHz and a frequency accuracy of 30~MHz. We partially resolve the hyperfine structure and measure the nuclear quadrupole coupling of the excited vibrational state.