Sulphur hexafluoride is a very strong greenhouse gas whose concentration is increasing in the atmosphere. It is detected through infrared absorption spectroscopy in the strong ν₃ fundamental region. Due to the existence of low-lying vibrational states of this molecule, however, many hot bands arise at room temperature and those are still not known. We present here a contribution to the elucidation of this hot band structure, by analysing the ν₂ + ν₃ combination band. We use a supersonic jet expansion high-resolution spectrum at a rotational temperature of ca. 25 K that was recorded thanks to the Jet-AILES setup at the Source Optimisée de Lumière d'Energie Intermédiaire du LURE (SOLEIL) Synchrotron. The simplified structure of this cold spectrum allowed us to assign 444 rovibrational lines and to fit effective Hamiltonian parameters, leading to a very satisfactory spectrum simulation. The parameters obtained in this way allow to calculate the spectrum of the ν₃+ν₂−ν₂ hot band.