Geochemical constraints on mantle temperature indicate a regular decrease by around 250 K since 3 Ga. However models of Earth’s cooling that rely on scaling laws for thermal convection without strong plates are facing a thermal runaway backwards in time, due to the power-law dependence of heat loss on temperature. To explore the effect of surface dynamics on Earth’s cooling rate, we build a 2D temperature-dependent model of plate tectonics that relies on a force balance for each plate and on Earth-like parameterized behaviors for the motion, creation and disappearance of plate boundaries. While our model predicts the expected thermal runaway if plate boundaries are fixed, we obtain an average cooling rate consistent with geochemical estimates if the geometry of plate tectonics evolves through time. For a warmer mantle in the past, plates are faster but also longer (and less numerous) so that the average seafloor age and resulting heat flux always remain moderate. The predicted increase in the number of plates forwards in time is in good agreement with recent plate reconstructions over the last 400 Myr. Our model also yields plate speed and subduction area flux consistent with these reconstructions. We finally compare the effect of parameters controlling mantle viscosity and individual plate speeds to the effect of localized surface processes, such as oceanization and subduction initiation. We infer that studies of Earth’s thermal history should focus on surface processes as they appear to be key control parameters.