We investigate whether there are variations of the central wavelengths or the profile shapes of diffuse interstellar bands and whether these variations are caused by different physical parameters of translucent clouds. For this purpose we used spectra of two stars seen through two different single clouds: HD 34078 (AE Aur) and HD 73882. The wavelength displacements of the diffuse interstellar bands at 6196 Å, 6203 Å, 6376 Å, 6379 Å and 6614 Å with respect to the well known interstellar atomic and molecular lines (KI and CH) were measured. The shift is seemingly absent in the diffuse interstellar bands at 4726 Å, 4964 Å, 4763 Å, and 4780 Å. In addition the considered profiles may show (in HD 34078) extended red wings. The observed phenomena are likely related to physical parameters of intervening clouds (rotational temperatures of molecular species) and may help in the identification of the diffuse interstellar band carriers.