Successful brazing using Cu-based nanostructured brazing fillers at temperatures much below the bulk melting temperature of Cu was recently demonstrated (Lehmert et al. in, Mater Trans 56:1015-1018, 2015. The Cu-based nano-fillers are composed of alternating nanolayers of Cu and a permeable, non-wetted AlN barrier. In this study, a thermodynamic model is derived to estimate the melting point depression (MPD) in such Cu/AlN nano-multilayers (NMLs) as function of the Cu nanolayer thickness. Depending on the melting route, the model predicts a MPD range of 238-609 K for Cu 10nm /AlN 10nm NMLs, which suggests a heterogeneous pre-melting temperature range of 750-1147 K (476-874°C), which is consistent with experimental observations. As suggested by basic kinetic considerations, the observed Cu outflow to the NML surface at the temperatures of 723-1023 K (450-750°C) can also be partially rationalized by fast solid-state diffusion of Cu along internal interfaces, especially for the higher temperatures.