Context. Planet traps and snow lines are structures that may promote planetary formation in protoplanetary disks. They are very sensitive to the disk density and temperature structure. It is therefore necessary to follow the time evolution of the disk thermal structure throughout its viscous spreading. Since the snowlines are thought to generate density and temperature bumps, it is important to take into account the disk opacity variations when the various dust elements are sublimated. Aims. We track the time evolution of planet traps and snowlines in a viscously evolving protoplanetary disk using an opacity table that accounts for the composition of the dust material. Methods. We coupled a dynamical and thermodynamical disk model with a temperature-dependent opacity table (that accounts for the sublimation of the main dust components) to investigate the formation and evolution of snowlines and planet traps during the first million years of disk evolution. Results. Starting from a minimum mass solar nebula, we find that the disk mid-plane temperature profile shows several plateaux (0.1−1 AU wide) at the different sublimation temperatures of the species that make up the dust. For water ice, the corresponding plateau can be larger than 1 AU, which means that this is a snow “region” rather than a snow “line”. As a consequence, the surface density of solids in the snow region may increase gradually, not abruptly. Several planet traps and desert regions appear naturally as a result of abrupt local changes in the temperature and density profiles over the disk lifetime. These structures are mostly located at the edges of the temperature plateaux (surrounding the dust sublimation lines) and at the heat-transition barrier where the disk stellar heating and viscous heating are of the same magnitude (around 10 AU after 1 Myr). Conclusions. Several traps are identified: although a few appear to be transient, most of them slowly migrate along with the heat-transition barrier or the dust sublimation lines. These planet traps may temporarily favor the growth of planetary cores.