On water‐dominated planets, warming from increased solar insolation is strongly amplified by the water vapor greenhouse feedback. As the Sun brightens due to stellar evolution, Earth will become uninhabitable due to rising temperatures. Here we use a modified version of the Community Earth System Model from the National Center for Atmospheric Research to study Earth under intense solar radiation. For small (≤10%) increases in the solar constant (S0), Earth warms nearly linearly with climate sensitivities of ~1 K/(W m−2) and global mean surface temperatures below 310 K. However, an abrupt shift in climate is found as the solar constant is increased to +12.5% S0. Here climate sensitivity peaks at ~6.5 K/(W m−2), while global mean surface temperatures rise above 330 K. This climatic transition is associated with a fundamental change to the radiative‐convective state of the atmosphere. Hot, moist climates feature both strong solar absorption and inefficient radiative cooling in the low atmosphere, thus yielding net radiative heating of the near‐surface layers. This heating forms an inversion that effectively shuts off convection in the boundary layer. Beyond the transition, Earth continues to warm but with climate sensitivities again near unity. Conditions conducive to significant water loss to space are not found until +19% S0. Earth remains stable against a thermal runaway up to at least +21% S0, but at that point, global mean surface temperatures exceed 360 K, and water loss to space becomes rapid. Water loss of the oceans from a moist greenhouse may preclude a thermal runaway. Key Points Increasing solar luminosity will render the Earth uninhabitable within ~2 Gyr A radiative‐convective transition marks the onset of a moist greenhouse A runaway greenhouse may never occur, precluded by rapid water loss