  The stability of Earth's climate on geological timescales is enabled by the
carbon-silicate cycle that acts as a negative feedback mechanism stabilizing
surface temperatures via the intake and outgas of atmospheric carbon. On Earth,
this thermostat is enabled by plate tectonics that sequesters outgassed CO2
back into the mantle via weathering and subduction at convergent margins. Here
we propose a separate tectonic mechanism -- vertical recycling -- that can
serve as the vehicle for CO2 outgassing and sequestration over long timescales.
The mechanism requires continuous tidal heating, which makes it particularly
relevant to planets in the habitable zone of M stars. Dynamical models of this
vertical recycling scenario and stability analysis show that temperate climates
stable over Gy timescales are realized for a variety of initial conditions,
even as the M star dims over time. The magnitude of equilibrium surface
temperatures depends on the interplay of sea weathering and outgassing, which
in turn depends on planetary carbon content, so that planets with lower carbon
budgets are favoured for temperate conditions. Habitability of planets such as
found in the Trappist-1 may be rooted in tidally-driven tectonics.
