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The dependence of plasmon resonance excitations in ultrafine (3-7 nm) gold nanoparticles on heating and melting is investigated. An integrated approach is adopted, where molecular dynamics simulations of the spatial and temporal development of the atoms constituting the nanoparticles generate trajectories out of which system conformations are sampled and extracted for calculations of plasmonic excitation cross sections which then are averaged over the sample configurations for the final result. The calculations of the plasmonic excitations, which take into account the temperature- and size-dependent relaxation of the plasmons, are carried out with a newly developed Extended Discrete Interaction Model (Ex-DIM) and complemented by multilayered Mie theory. The integrated approach clearly demonstrates the conditions for suppression of the plasmons starting at temperatures well below the melting point. We have found a strong inhomogeneous dependence of the atom mobility in the particle crystal lattice increasing from the center to its surface upon the temperature growth. The plasmon resonance suppression is associated with an increase of the mobility and in the amplitude of phonon vibrations of the lattice atoms accompanied by electron-phonon scattering. This leads to an increase in the relaxation constant impeding the plasmon excitation as the major source of the suppression, while the direct contribution from the increase in the lattice constant and its chaotization at melting is found to be minor. Experimental verification of the suppression of surface plasmon resonance is demonstrated for gold nanoparticles on a quartz substrate heated up to the melting temperature and above.