Unlike on present day Mars, for pressures higher than a fraction of a bar, surface temperatures vary with altitude because of the adiabatic cooling and warming of the atmosphere when it moves vertically. In most simulations, CO₂ ice clouds cover a major part of the planet. Previous studies had suggested that they could have warmed the planet thanks to their scattering greenhouse effect. However, even assuming parameters that maximize this effect, it does not exceed +15 K. Combined with the revised CO₂ spectroscopy and the impact of surface CO₂ ice on the planetary albedo, we find that a CO₂ atmosphere could not have raised the annual mean temperature above 0°C anywhere on the planet. The collapse of the atmosphere into permanent CO₂ ice caps is predicted for pressures higher than 3 bar, or conversely at pressure lower than one bar if the obliquity is low enough. Summertime diurnal mean surface temperatures above 0°C (a condition which could have allowed rivers and lakes to form) are predicted for obliquity larger than 40° at high latitudes but not in locations where most valley networks or layered sedimentary units are observed. In the absence of other warming mechanisms, our climate model results are thus consistent with a cold early Mars scenario in which non climatic mechanisms must occur to explain the evidence for liquid water. In a companion paper by Wordsworth et al., we simulate the hydrological cycle on such a planet and discuss how this could have happened in more detail.