(Abridged) Aims: We aim to use the progressive heating of the gas caused by the feedback of high-mass young stellar objects (YSOs) to prove the statistical validity of the most common schemes used to define an evolutionary sequence for high-mass clumps, and characterise the sensitivity of different tracers to this process. Methods: From the spectroscopic follow-ups of the ATLASGAL TOP100 sample, we selected several multiplets of CH3CN, CH3CCH, and CH3OH emission lines to derive and compare the physical properties of the gas in the clumps along the evolutionary sequence. Our findings are compared with results obtained from CO isotopologues, dust, and NH3 from previous studies on the same sample. Results: The chemical properties of each species have a major role on the measured physical properties. Low temperatures are traced by NH3, CH3OH, and CO (in the early phases), the warm and dense envelope can be probed with CH3CN, CH3CCH, and, in evolved sources via CO isotopologues. CH3OH and CH3CN are also abundant in the hot cores, and their high-excitation transitions may be good tools to study the kinematics in the hot gas surrounding the YSOs that these clumps are hosting. All tracers show, to different degrees, progressive warming with evolution. The relation between gas temperature and L/M is reproduced by a toy model of a spherical, internally heated clump. Conclusions: The evolutionary sequence defined for the clumps is statistically valid and we could identify the processes dominating in different intervals of L/M. For L/M<2Lsun/Msun a large quantity of gas is still being accumulated and compressed at the bottom of the potential well. Between 2Lsun/Msun<L/M<40Lsun/Msun the YSOs gain mass and increase in L; the first hot cores appear around L/M=10Lsun/Msun. Finally, for L/M>40Lsun/Msun HII regions become common, showing that dissipation of the parental clump dominates.
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