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Aims. Hard X-ray spectra of black hole binaries (BHB) are produced by Comptonization of soft seed photons by hot electrons near the black hole. The slope of the resulting energy spectra is governed by two main parameters: the electron temperature (Te) and optical depth (τ) of the emitting plasma. Given the extreme brightness of V404 Cyg during the 2015 outburst, we aim to constrain the source spectral properties using an unprecedented time resolution in hard X-rays, and to monitor the evolution of Te and τ over the outburst. Methods. We have extracted and analysed 602 X-ray spectra of V404 Cyg obtained by the IBIS/ISGRI instrument on-board INTEGRAL during the 2015 June outburst, using effective integration times ranging between 8 and 176 000 s. We fitted the resulting spectra in the 20-200 keV energy range. Results. We find that while the light curve and soft X-ray spectra of V404 Cyg are remarkably different from those of other BHBs, the spectral evolution of V404 Cyg in hard X-rays and the relations between the spectral parameters are consistent with those observed in other BHBs. We identify a hard branch in which the Te is anti-correlated with the hard X-ray flux, and a soft flaring branch in which the relation reverses. In addition, we find that during long X-ray plateaus detected at intermediate fluxes, the thermal Comptonization models fail to describe the spectra. However, the statistics improve if we allow NH to vary freely in the fits to these spectra. Conclusions. We conclude that the hard branch in V404 Cyg is analogous to the canonical hard state of BHBs. V404 Cyg never seems to enter the canonical soft state, although the soft flaring branch bears resemblance to the BHB intermediate state and ultraluminous state. The X-ray plateaus are likely the result of absorption by a Compton-thick outflow (NH ≥ 1024 cm-22) which reduces the observed flux by a factor of about 10. Variable covering of the central source by this Compton-thick material may be the reason for the complicated light curve variability, rather than intrinsic source variability. [ABSTRACT FROM AUTHOR]