In this study, we investigate how physical properties, such as the density and temperature profiles, evolve on core scales through the evolutionary sequence during high-mass star formation ranging from protostars in cold infrared dark clouds to evolved UCHII regions. We observed 11 high-mass star-forming regions with ALMA at 3 mm wavelengths. Based on the 3 mm continuum morphology and recombination line emission, tracing locations with free-free (ff) emission, the fragmented cores analyzed in this study are classified into either dust or dust+ff cores. In addition, we resolve three cometary UCHII regions with extended 3 mm emission that is dominated by free-free emission. The temperature structure and radial profiles (T~r^-q ) are determined by modeling molecular emission of CH3CN and CH313CN with XCLASS and by using the HCN-to- HNC intensity ratio as probes for the gas kinetic temperature. The density profiles (n~r^-p ) are estimated from the 3 mm continuum visibility profiles. The masses M and H2 column densities N(H2) are then calculated from the 3 mm dust continuum emission. Results. We find a large spread in mass and peak H2 column density in the detected sources ranging from 0.1-150 Msun and 10^23 - 10^26 cm-2 , respectively. Including the results of the CORE and CORE-extension studies (Gieser et al. 2021, 2022) to increase the sample size, we find evolutionary trends on core scales for the temperature power-~law index q increasing from 0.1 to 0.7 from infrared dark clouds to UCHII regions, while for the the density power-law index p on core scales, we do not find strong evidence for an evolutionary trend. However, we find that on the larger clump scales throughout these evolutionary phases the density profile flattens from p = 2.2 to p = 1.2. (abridged)