ALMA-IMF XVI. Mass-averaged temperature of cores and protostellar luminosities in the ALMA-IMF protoclusters

Context. The ALMA-IMF Large Program imaged 15 massive protoclusters down to a resolution of similar to 2 kau scales, identifying about 10(3) star-forming cores. The mass and luminosity of these cores, which are fundamental physical characteristics, are difficult to determine, a problem greatly exacerbated at the distances >= 2 kpc of ALMA-IMF protoclusters. Aims. We combined new datasets and radiative transfer modeling to characterize these cores. We estimated their mass-averaged temperature and the masses these estimates imply. For one-sixth of the sample, we measured the bolometric luminosities, implementing deblending corrections when necessary. Methods. We used spectral energy distribution (SED) analysis obtained with the point process mapping (PPMAP) Bayesian procedure, which aims to preserve the best angular resolution of the input data. We extrapolated the luminosity and dust temperature images provided by PPMAP at 2.5 '' resolution to estimate those of individual cores, which were identified at higher angular resolution. To do this, we applied approximate radiative transfer relationships between the luminosity of a protostar and the temperature of its surrounding envelope and between the external heating of prestellar cores and their temperatures. Results. For the first time, we provide data-informed estimates of dust temperatures for 882 cores identified with ALMA-IMF: 17-31 K and 28-79 K (5th and 95th percentiles, up to 127 K) for the 616 prestellar and 266 protostellar cores, respectively. We also measured protostellar luminosities spanning 20-80 000 L-circle dot. Conclusions. Dust temperatures previously estimated from SED-based analyses at a comparatively lower resolution validate our method. For hot cores, on the other hand, we estimated systematically lower temperatures than studies based on complex organic molecules. We established a mass-luminosity evolutionary diagram, for the first time at the core spatial resolution and for a large sample of intermediate- to high-mass protostellar cores. The ALMA-IMF data favor a scenario in which protostars accrete their mass from a larger mass reservoir than their host cores.