Sulfur hexafluoride is a greenhouse gas with a long lifetime in the atmosphere and an important tracer for air mass circulation atmospheric models. The IR spectrum of this heavy species, however, features many hot bands at room temperature (at which only 30% of the molecules lie in the ground vibrational state), especially those originating from the lowest, v6 and v5=1 vibrational states. Using a cryogenic long path cell with variable optical path length and temperatures regulated between 168 and 163 K, coupled to Synchrotron Radiation and a high resolution interferometer, Doppler-limited spectra of the very weak ν3+ν5 band near 1450 cm−1 have been recorded. Low temperature was used to limit the presence of hot bands and simplify the rotational structure. The spectrum has been analyzed thanks to the XTDS software package. Combining with the results obtained previously on the weak difference bands in the far infrared region involving the v5=1 states, we are thus able to use the tensorial model to propose a spectroscopic parameter set for modelling the strong ν3+ν5-ν5 hot band. The model constitutes a coherent set of molecular parameters and enable spectral simulation for atmospheric sounding. Test simulations at different temperatures and in nitrogen broadened conditions are presented and compared with new experimental cross section data for the absorption region relevant for atmospheric quantification.