We present the Voigt profile analysis of 132 intervening CIV+CIII components associated with optically thin HI absorbers at 2.1<z<3.4 in the 19 high-quality UVES/VLT and HIRES/Keck QSO spectra. For logN_CIV_ in [11.7, 14.1], N_CIII_{propto}N_CIV_^1.42+/-0.11^ and <N_CIII}/N_CIV>=1.0+/-0.3 with a negligible redshift evolution. For 54 CIV components tied (aligned) with HI at logN_HI_ in [12.2, 16.0] and logN_CIV_ in [11.8, 13.8], the gas temperature T_b_ estimated from absorption line widths is well approximated to a Gaussian peaking at logT_b_~4.4+/-0.3 for logT_b_ in [3.5, 5.5], with a negligible non-thermal contribution. For 32 of 54 tied HI+CIV pairs, also tied with CIII at logN_CIII_ in [11.7, 13.8], we ran both photoionization equilibrium (PIE) and non-PIE (using a fixed temperature T_b_) cloudy models for the Haardt-Madau QSOs+galaxies 2012 UV background. We find evidence of bimodality in observed and derived physical properties. High-metallicity branch absorbers have a carbon abundance [C/H]temp>=-1.0, a line-of-sight length L_temp_<=20kpc and a total (neutral and ionized) hydrogen volume density logn_H,temp_ in [-4.5, -3.3] and logT_b_ in [3.9, 4.5]. Low-metallicity branch absorbers have [C/H]temp<=-1.0, L_temp_ in [20, 480]kpc and logn_H,temp_ in [-5.2, -4.3] and logT_b_~ 4.5. High-metallicity branch absorbers seem to be originated from extended discs, inner haloes or outflowing gas of intervening galaxies, while low-metallicity absorbers are produced by galactic haloes or the surrounding intergalactic medium filament.