Methodology used to estimate the mass-averaged dust temperature of ALMA-IMF cores: luminous protostellar cores (left panels), low-luminosity protostellar cores (central panels), and prestellar cores (right panels). Sketch (upper panels) and radial profile (lower panels) representing the mass-averaged dust temperature of a given core, as estimated by constraints obtained outside the core and, for the luminous protostars, within the core. The absolute values of the equations, the mean $\overline{T_{\text{dust }}}$, and its uncertainty that are used for illustration are those computed for three cores of the W43-MM1 protocluster: core #1 for luminous protostars, core #26 for low-luminosity protostars, and core #6 for prestellar cores. In the left panels, for luminous protostellar cores, the mass-averaged dust temperature was computed with two approaches. The temperature was first measured in PPMAP images at a radius of 1.25″ and extrapolated within the PPMAP beam to the outer radius of the core, R_out (blue area and blue equation). Its value at R_out was also computed from the internal heating of the protostar with a luminosity of L_proto⋆ (orange area and orange equation). In the central panel, for low-luminosity protostellar cores, the mass-averaged dust temperature measured in PPMAP images at a radius of 1.25″ is extrapolated within the PPMAP beam to the outer radius of the core, R_out (blue area and blue equation). In the right panels, for prestellar cores, the mass-averaged dust temperature measured in PPMAP images at a radius of 1.25″ is extrapolated within the PPMAP beam to the outer radius of the core, R_out (orange area and orange equation). The mathematical relationships describing the mass-averaged temperature expected for the inner parts of low-luminosity protostellar cores and prestellar cores are not used in the present study.