CUPID-0 is the first large mass array of enriched Zn 82 Se scintillating low temperature calorimeters, operated at LNGS since 2017. During its first scientific runs, CUPID-0 collected an exposure of 9.95 kg year. Thanks to the excellent rejection of α particles, we attained the lowest background ever measured with thermal detectors in the energy region where we search for the signature of 82 Se neutrinoless double beta decay. In this work we develop a model to reconstruct the CUPID-0 background over the whole energy range of experimental data. We identify the background sources exploiting their distinctive signatures and we assess their extremely low contribution down to ∼ 10 - 4 counts/(keV kg year) in the region of interest for 82 Se neutrinoless double beta decay search. This result represents a crucial step towards the comprehension of the background in experiments based on scintillating calorimeters and in next generation projects such as CUPID.