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 to better understand the physical mechanisms that lead galaxy migrations in this space . Aims : In this paper we try to bring new clues by 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 using the SED best fit template on the COSMOS primary photometric catalogues ) . Combining these two measurements with spectroscopic redshifts from the zCOSMOS 10k release , we isolate 210 I _ { AB } < 22 blue early-type galaxies with M _ { * } / M _ { \odot } > 10 ^ { 10 } in three redshift bins ( 0.2 < z < 0.55 , 0.55 < z < 0.8 , 0.8 < z < 1.4 ) and study the evolution of their properties ( number density , SFR , morphology , size ) . Results : The threshold mass ( M _ { t } ) 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 _ { \odot } ) \sim 10.1 \pm 0.35 at z \sim 0.3 to log ( M _ { * } / M _ { \odot } ) \sim 10.9 \pm 0.35 at z \sim 1 . Interestingly it follows the evolution of the crossover mass between the early and late type population ( 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 _ { \odot } ) \sim 10.8 blue E/S0 resemble to merger remnants probably migrating to the red-sequence in a time-scale of \sim 3 Gyr . Below this mass , they seem to be closer to normal late-type galaxies as if they were the result of minor mergers which 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 \sim 1 in contrast with the threshold mass and therefore does not seem to be linked with the relative abundance of blue E/S0s . Conclusions :