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The paper describes profile broadening and peak wavelength variation of diffuse interstellar bands (DIBs) measured for 46 lines of sight, probably caused by physical properties of intervening clouds. Full width at half maximum of four studied diffuse bands (5780, 5797, 6196 and 6614 Å) demonstrate strong variability sometimes doubling the features' width. Despite the high magnitude of the effect, our current analysis is restricted to the strongest diffuse bands because the weaker ones require a much higher S/N ratio. The profile broadening in the studied DIBs moves the profile's centers towards longer wavelengths, probably due to the excitation of higher levels of the P branch of the unknown molecular carrier. Moreover, diffuse bands are broader in clouds with abundantly populated vibrationally excited states of the hydrogen molecules, i.e. DIB's broadening correlates with the rotational temperature estimated on H$_2$ $ν$=2 vibrational level. However, objects demonstrating extremely broadened profiles of DIBs are scarce. The extreme peculiarity of DIBs' profiles was detected in Herschel~36. Here we show the gradual growths of the widths of diffuse bands, confirmed in spectra from different instruments.