[1] The thermal evolution of magma oceans produced by collision with giant impactors late in accretion is expected to depend on the composition and structure of the atmosphere through the greenhouse effect of CO 2 and H 2 O released from the magma during its crystallization. In order to constrain the various cooling timescales of the system, we developed a 1-D parameterized convection model of a magma ocean coupled with a 1-D radiative-convective model of the atmosphere. We conducted a parametric study and described the influences of the initial volatile inventories, the initial depth of the magma ocean, and the Sun-planet distance. Our results suggest that a steam atmosphere delays the end of the magma ocean phase by typically 1 Myr. Water vapor condenses to an ocean after 0.1, 1.5, and 10 Myr for, respectively, Mars, Earth, and Venus. This time would be virtually infinite for an Earth-sized planet located at less than 0.66 AU from the Sun. Using a more accurate calculation of opacities, we show that Venus is much closer to this threshold distance than in previous models. So there are conditions such as no water ocean is formed on Venus. Moreover, for Mars and Earth, water ocean formation timescales are shorter than typical time gaps between major impacts. This implies that successive water oceans may have developed during accretion, making easier the loss of their atmospheres by impact erosion. On the other hand, Venus could have remained in the magma ocean stage for most of its accretion.

How the volatile content influences the primordial surface conditions of terrestrial planets and, thus, their future geodynamic evolution is an important question to answer. We simulate the secular convective cooling of a 1‐D magma ocean (MO) in interaction with its outgassed atmosphere. The heat transfer in the atmosphere is computed either using the grey approximation or using a k‐correlated method. We vary the initial CO2 and H2O contents (respectively from 0.1 × 10−2 to 14 × 10−2 wt % and from 0.03 to 1.4 times the Earth Ocean current mass) and the solar distance—from 0.63 to 1.30 AU. A first rapid cooling stage, where efficient MO cooling and degassing take place, producing the atmosphere, is followed by a second quasi steady state where the heat flux balance is dominated by the solar flux. The end of the rapid cooling stage (ERCS) is reached when the mantle heat flux becomes negligible compared to the absorbed solar flux. The resulting surface conditions at ERCS, including water ocean's formation, strongly depend both on the initial volatile content and solar distance D. For D > DC, the “critical distance,” the volatile content controls water condensation and a new scaling law is derived for the water condensation limit. Although today's Venus is located beyond DC due to its high albedo, its high CO2/H2O ratio prevents any water ocean formation. Depending on the formation time of its cloud cover and resulting albedo, only 0.3 Earth ocean mass might be sufficient to form a water ocean on early Venus.