Evolution of the surface temperature for a: an oxygen fugacity at the IW buffer and different initial mantle concentrations of water (in different shades of blue), b: an initial mantle concentration of water of 500 ppm and different oxygen fugacities (in different shades of yellow and red) of an Earth-sized stagnant-lid planet located at 1 au around the evolving Sun. The reference scenario (T_m,0 = 1700 K, , and f_O2 at the IW buffer) is indicated in black. The freezing point of water (273 K) is indicated by the dashed black line in both panels. The temperatures in panel a correspond to the outgassing evolutions of H₂O and CO₂ plotted in Figs. 6c and d, while the temperatures of panel b correspond to the outgassing evolutions of Figs. 8a and b.