  We report the discovery of planet Kepler-12b (KOI-20), which at 1.695\pm0.030
RJ is among the handful of planets with super-inflated radii above 1.65 RJ.
Orbiting its slightly evolved G0 host with a 4.438-day period, this
0.431\pm0.041 MJ planet is the least-irradiated within this
largest-planet-radius group, which has important implications for planetary
physics. The planet's inflated radius and low mass lead to a very low density
of 0.111\pm0.010 g cm-3. We detect the occultation of the planet at a
significance of 3.7{\sigma} in the Kepler bandpass. This yields a geometric
albedo of 0.14\pm0.04; the planetary flux is due to a combination of scattered
light and emitted thermal flux. We use multiple observations with Warm Spitzer
to detect the occultation at 7{\sigma} and 4{\sigma} in the 3.6 and 4.5 {\mu}m
bandpasses, respectively. The occultation photometry timing is consistent with
a circular orbit, at e < 0.01 (1{\sigma}), and e < 0.09 (3{\sigma}). The
occultation detections across the three bands favor an atmospheric model with
no dayside temperature inversion. The Kepler occultation detection provides
significant leverage, but conclusions regarding temperature structure are
preliminary, given our ignorance of opacity sources at optical wavelengths in
hot Jupiter atmospheres. If Kepler-12b and HD 209458b, which intercept similar
incident stellar fluxes, have the same heavy element masses, the interior
energy source needed to explain the large radius of Kepler-12b is three times
larger than that of HD 209458b. This may suggest that more than one
radius-inflation mechanism is at work for Kepler-12b, or that it is less
heavy-element rich than other transiting planets.
