Rapid developments in nanoengineering calls for characterization methods capable to reach high spatial resolution. In this domain, scanning transmission electron microscope (STEM) provides a broad scale of measurement techniques ranging from Z-contrast or electron energy- loss elemental mapping, differential phase contrast, via local electronic structure studies of single atoms to counting individual atoms in nanoparticles. As a specific case of high-spatial resolution electron energy-loss spectroscopy (EELS), vibrational EELS became possible only since 2014, when the new electron beam monochromators allowed to reach better than 10 meV energy resolution. Rapid developments in this area lead to work demonstrating atomic level contrast in the vibrational EELS. Theoretical description of vibrational EELS uses prohibitively time consuming quantum-mechanical models to describe phonon spectra and single or multiple phonon excitation processes. We intend to perform simulations using colored thermostats, which will dramatically reduce the required computing time and allow to simulate realistic situations and address fundamental questions in vibrational STEM-EELS related to delocalization of phonon signals, actual spatial resolution, mapping of phonon dispersions to energy- and angle-resolved measurements, etc.