  We present an analysis and interpretation of the Kepler binary system KOI
1224. This is the fourth binary found with Kepler that consists of a thermally
bloated, hot white dwarf in a close orbit with a more or less normal star of
spectral class A or F. As we show, KOI 1224 contains a white dwarf with Teff =
14400 +/- 1100 K, mass = 0.20 +/- 0.02 Msun, and radius = 0.103 +/- 0.004 Rsun,
and an F-star companion of mass = 1.59 +/- 0.07 Msun that is somewhat beyond
its terminal-age main sequence. The orbital period is quite short at 2.69802
days. The ingredients that are used in the analysis are the Kepler binary light
curve, including the detection of the Doppler boosting effect; the NUV and FUV
fluxes from the Galex images of this object; an estimate of the spectral type
of the F-star companion; and evolutionary models of the companion designed to
match its effective temperature and mean density. The light curve is modelled
with a new code named Icarus which we describe in detail. Its features include
the full treatment of orbital phase-resolved spectroscopy, Doppler boosting,
irradiation effects and transits/eclipses, which are particularly suited to
irradiated eclipsing binaries. We interpret the KOI 1224 system in terms of its
likely evolutionary history. We infer that this type of system, containing a
bloated hot white dwarf, is the direct descendant of an Algol-type binary. In
spite of this basic understanding of the origin of KOI 1224, we discuss a
number of problems associated with producing this type of system with this
short of an short orbital period.
