  Since the discovery of the first transiting hot Jupiters, models have sought
to explain the anomalously large radii of highly irradiated gas giants. We now
know that the size of hot Jupiter radius anomalies scales strongly with a
planet's level of irradiation and numerous models like tidal heating, ohmic
dissipation, and thermal tides have since been developed to help explain these
inflated radii. In general however, these models can be grouped into two broad
categories: 1) models that directly inflate planetary radii by depositing a
fraction of the incident irradiation into the interior and 2) models that
simply slow a planet's radiative cooling allowing it to retain more heat from
formation and thereby delay contraction. Here we present a new test to
distinguish between these two classes of models. Gas giants orbiting at
moderate orbital periods around post main sequence stars will experience
enormous increases their irradiation as their host stars move up the sub-giant
and red-giant branches. If hot Jupiter inflation works by depositing
irradiation into the planet's deep interiors then planetary radii should
increase in response to the increased irradiation. This means that otherwise
non-inflated gas giants at moderate orbital periods >10 days can re-inflate as
their host stars evolve. Here we explore the circumstances that can lead to the
creation of these "re-inflated" gas giants and examine how the existence or
absence of such planets can be used to place unique constraints of the physics
of the hot Jupiter inflation mechanism. Finally, we explore the prospects for
detecting this potentially important undiscovered population of planets.
