In this paper, we present new data with interstellar C2 (Phillips bands A-X), from observations made with the Ultraviolet-Visual Echelle Spectrograph of the European Southern Observatory. We have determined the interstellar column densities and excitation temperatures of C2 for nine Galactic lines. For seven of these, C2 has never been observed before, so in this case the still small sample of interstellar clouds (26 lines of sight), where a detailed analysis of C2 excitation has been made, has increased significantly. This paper is a continuation of previous works where interstellar molecules (C2 and diffuse interstellar bands) have been analysed. Because the sample of interstellar clouds with C2 has increased, we can show that the width and shape of the profiles of some diffuse interstellar bands (6196 and 5797 A) apparently depend on the gas kinetic and rotational temperatures of C2; the profiles are broader because of the higher values of the gas kinetic and rotational temperatures of C2. There are also diffuse interstellar bands (4964 and 5850 A) for which this effect does not exist.