Context. High-mass star formation is a hierarchical process from cloud (>1 pc), to clump (0.1−1 pc), to core scales (<0.1 pc). Modern interferometers that achieve high angular resolutions at millimeter wavelengths allow us to probe the physical and chemical properties of the gas and dust of protostellar cores in the earliest evolutionary formation phases. Aims. 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 ultracompact HII (UCHII) regions. Methods. We observed 11 high-mass star-forming regions with the Atacama Large Millimeter/submillimeter Array (ALMA) at 3 mm wavelengths. Based on the 3 mm continuum morphology and H(40)α recombination line emission - which trace locations with free-free (ff) emission - the fragmented cores analyzed in this study are classified as either “dust” or “dust+ff” cores. In addition, we resolved 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) were determined by modeling the molecular emission of CH3CN and CH313CN with XCLASS and by using the HCN-to-HNC intensity ratio as a probe for the gas kinetic temperature. The density profiles (n ~ r−p) were estimated from the 3 mm continuum visibility profiles. The masses (M) and H2 column densities (N(H2)) were 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 to 150 M⊙ and 1023 to 1026 cm−2, respectively. Including the results of the CORE and CORE-extension studies 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 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 the density profile flattens from p ≈ 2.2 to p ≈ 1.2 during these evolutionary phases. Conclusions. By characterizing a large statistical sample of individual fragmented cores, we find that the physical properties, such as the temperature on core scales and the density profile on clump scales, evolve even during the earliest evolutionary phases in high-mass star-forming regions. These findings provide observational constraints for theoretical models that describe the formation of massive stars. In follow-up studies we aim to further characterize the chemical properties of the regions by analyzing the large amount of molecular lines detected with ALMA in order to investigate how the chemical properties of the molecular gas evolve during the formation of massive stars.