We report on the measurement of the two-neutrino double-β decay of 82 Se performed for the first time with cryogenic calorimeters, in the framework of the CUPID-0 experiment. With an exposure of 9.95 kg yr of Zn 82 Se, we determine the two-neutrino double-β decay half-life of 82 Se with an unprecedented precision level, T 2ν 1=2 ¼ ½8.60 AE 0.03ðstatÞ þ0.19 −0.13 ðsystÞ × 10 19 yr. The very high signal-to-background ratio, along with the detailed reconstruction of the background sources allowed us to identify the single state dominance as the underlying mechanism of such a process, demonstrating that the higher state dominance hypothesis is disfavored at the level of 5.5σ.