a) Luminosity evolution profiles for different power-law indices. b) Temperature evolution in the hot core model hmc-r3 at different radii: ~200 AU (blue), ~2000 AU (green) and ~10 000 AU (red). Temperature distribution obtained using different protostellar luminosity evolutions are shown with continuous (l2), dashed (l4), and dotted (l7) lines. c) Spatio-temporal evolution of the temperature in the hot core model hmc-r3.