  Many giant exoplanets in close orbits have observed radii which exceed
theoretical predictions. One suggested explanation for this discrepancy is heat
deposited deep inside the atmospheres of these "hot Jupiters". Here, we study
extended power sources which distribute heat from the photosphere to the deep
interior of the planet. Our analytical treatment is a generalization of a
previous analysis of localized "point sources". We model the deposition profile
as a power law in the optical depth and find that planetary cooling and
contraction halt when the internal luminosity (i.e. cooling rate) of the planet
drops below the heat deposited in the planet's convective region. A slowdown in
the evolutionary cooling prior to equilibrium is possible only for sources
which do not extend to the planet's center. We estimate the Ohmic dissipation
resulting from the interaction between the atmospheric winds and the planet's
magnetic field, and apply our analytical model to Ohmically heated planets. Our
model can account for the observed radii of most inflated planets which have
equilibrium temperatures $\approx 1500\textrm{K}-2500\textrm{K}$, and are
inflated to a radius $\approx 1.6 R_J$. However, some extremely inflated
planets remain unexplained by our model. We also argue that Ohmically inflated
planets have already reached their equilibrium phase, and no longer contract.
Following Wu & Lithwick who argued that Ohmic heating could only suspend and
not reverse contraction, we calculate the time it takes Ohmic heating to
re-inflate a cold planet to its equilibrium configuration. We find that while
it is possible to re-inflate a cold planet, the re-inflation timescales are
longer by a factor of $\approx 30$ than the cooling time.
