  Time-dependent insolation in a planetary atmosphere induces a mass quadrupole
upon which the stellar tidal acceleration can exert a force. This "thermal
tide" force can give rise to secular torques on the planet and orbit as well as
radial forces causing eccentricity evolution. We apply this idea to the
close-in gas giant exoplanets ("hot Jupiters"). The response of radiative
atmospheres is computed in a hydrostatic model which treats the insolation as a
time-dependent heat source, and solves for thermal radiation using flux-limited
diffusion. Fully nonlinear numerical simulations are compared to solutions of
the linearized equations, as well as analytic approximations, all of which are
in good agreement. We find generically that thermal tide density perturbations
{\it lead} the semi-diurnal forcing. As a result thermal tides can generate
asynchronous spin and eccentricity. Our results are as follows: (1) Departure
from synchronous spin is significant for hot Jupiters, and increases with
orbital period. (2) Ongoing gravitational tidal dissipation in spin equilibrium
leads to steady-state internal heating rates up to $\sim 10^{28} {\rm erg\
s^{-1}}$. If deposited sufficiently deep, these heating rates may explain the
anomalously large radii of many hot Jupiters in terms of a "tidal main
sequence" where cooling balances tidal heating. At fixed stellar type, planet
mass and tidal $Q$, planetary radius increases strongly toward the star inside
orbital periods $\la 2$ weeks. (3) There exists a narrow window in orbital
period where small eccentricities, $e$, grow exponentially with a large rate.
This window may explain the $\sim 1/4$ of hot Jupiters which should have been
circularized by the gravitational tide long ago, but are observed to have
significant nonzero $e$.(Abridged)
