Dimmings or transient coronal holes (i.e. regions of decreased intensity of soft X-ray and EUV emission), which are observed on the solar disk after halo coronal mass ejections (CMEs), are analyzed using SOHO/EIT data simultaneously in three coronal lines Fe IX/X (171 A), Fe XII (195 A) and Fe IX (284 A) sensitive to temperatures Te~1.2, 1.5 and 2.0 MK, respectively, as well as in the transition region line He II (304 A; Te~(0.02-0.08) MK). The analysis of rerotated difference images with 6- or 12-hour intervals and prior compensation of the solar rotation shows that usually the dimmings are most pronounced and have similar large-scale structures in the moderate-temperature coronal lines 171 and 195 A, while in the higher-temperature 284 A line the deepest dimming fragments are mainly visible. Many on-disk CME events show also clear, but relatively small-area dimming manifestations in 304 A line particularly at the background regions joining to a main eruption source. Moreover, there are events displaying transition region dimming patches that have no dimming counterparts in the coronal lines. These results suggest that in course of a CME process, opening of the magnetic field lines resulting in density depletion can also extend into cooler plasma of the transition region. Effects of temperature variations also cannot be ruled out for some dimming structures.