  Tidal friction in exoplanet systems, driven by orbits that allow for durable
nonzero eccentricities at short heliocentric periods, can generate internal
heating far in excess of the conditions observed in our own solar system.
Secular perturbations or a notional 2:1 resonance between a Hot Earth and Hot
Jupiter can be used as a baseline to consider the thermal evolution of
convecting bodies subject to strong viscoelastic tidal heating. We compare
results first from simple models using a fixed Quality factor and Love number,
and then for three different viscoelastic rheologies: the Maxwell body, the
Standard Anelastic Solid, and the Burgers body. The SAS and Burgers models are
shown to alter the potential for extreme tidal heating by introducing the
possibility of new equilibria and multiple response peaks. We find that tidal
heating tends to exceed radionuclide heating at periods below 10-30 days, and
exceed insolation only below 1-2 days. Extreme cases produce enough tidal heat
to initiate global-scale partial melting, and an analysis of tidal limiting
mechanisms such as advective cooling for earthlike planets is discussed. To
explore long term behaviors, we map equilibria points between convective heat
loss and tidal heat input as functions of eccentricity. For the periods and
magnitudes discussed, we show that tidal heating, if significant, is generally
detrimental to the width of habitable zones.
