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 > D_C, 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 D_C 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.