A challenging problem in gamma-ray spectrum analysis is the rapid detection of artificial radionuclides at low activity levels. Until now, traditional methods focus on activity estimation based on single spectra, obtained by integrating over time the measured disintegration events. However, accounting for the wellconstrained radionuclides decay should allow for a more accurate and sensitive activity estimation. For that purpose, we investigate a novel approach to estimate radionuclides' activity, which is i) first based on multi-temporal data, obtained from several short measurements rather than a single one, and ii) built upon a dedicated spectral unmixing, which allows processing multi-temporal data. The proposed algorithm allows accounting for both the full spectrum of each radionuclide (i.e. peaks and Compton continuum) and their activity decay in time. To that purpose, different approaches are investigated to model the temporal dependencies of the radionuclides' activities, and specifically to account for potentially out of equilibrium radionuclides' decay chains. Experimental results on both simulated spectra and real measurements are presented and compared to standard methods, it is shown that the proposed approach leads to more accurate estimations and faster detection of artificial radionuclides.