Context. Studying outliers from the bimodal distribution of galaxies in the color-mass space, such as morphological early-type galaxies residing in the blue cloud (blue E/S0s), can help for better understanding the physical mechanisms that lead galaxy migrations in this space. Aims: In this paper we try to bring new clues to studying the evolution of the properties of a significant sample of blue E/S0 galaxies in the COSMOS field. Methods: We define blue E/S0 galaxies as objects having a clear early-type morphology on the HST/ACS images (according to our automated classification scheme galSVM) but with a blue rest-frame color (defined by using the SED best-fit template on the COSMOS primary photometric catalogs). Combining these two measurements with spectroscopic redshifts from the zCOSMOS 10k release, we isolated 210 IAB < 22 blue early-type galaxies with M_*/M_&sun; > 1010 in three redshift bins (0.2 < z < 0.55, 0.55 < z < 0.8, 0.8 < z < 1.4) and studied the evolution of their properties (number density, SFR, morphology, size). Results: The threshold mass (Mt), defined at z = 0 in previous studies as the mass below which the population of blue early-type galaxies starts to be abundant relative to passive E/S0s, evolves from log (M_*/M_&sun;) ~ 10.1 ± 0.35 at z ~ 0.3 to log (M_*/M_&sun;) ~ 10.9 ± 0.35 at z ~ 1. Interestingly, it follows the evolution of the crossover mass between the early and late type populations (bimodality mass) indicating that the abundance of blue E/S0 is another measure of the downsizing effect in the build-up of the red sequence. There seems to be a turn-over mass in the nature of blue E/S0 galaxies. Above log (M_*/M_&sun;) ~ 10.8 blue E/S0 resemble to merger remnants probably migrating to the red sequence on a time scale of ˜3 Gyr. Below this mass, they seem to be closer to normal late-type galaxies, as if they were the result of minor mergers that triggered the central star formation and built a central bulge component or were (re)building a disk from the surrounding gas in a much longer time scale, suggesting that they are moving back or staying in the blue cloud. This turn-over mass does not seem to evolve significantly from z ~ 1 in contrast to the threshold mass and therefore does not seem to be linked with the relative abundance of blue E/S0s.