  In the hot-start core accretion formation model for gas giants, the interior
of a planet is usually assumed to be fully convective. By calculating the
detailed internal evolution of a planet assuming hot start outer boundary
conditions, we show that such a planet will in fact form with a radially
increasing internal entropy profile, so that its interior will be radiative
instead of convective. For a hot outer boundary, there is a minimum value for
the entropy of the internal adiabat $S_{min}$ below which the accreting
envelope does not match smoothly onto the interior, but instead deposits high
entropy material onto the growing interior. One implication of this would be to
at least temporarily halt the mixing of heavy elements within the planet, which
are deposited by planetesimals accreted during formation. The compositional
gradient this would impose could subsequently disrupt convection during
post-accretion cooling, which would alter the observed cooling curve of the
planet. However even with a homogeneous composition, for which convection
develops as the planet cools, the difference in cooling timescale will change
the inferred mass of directly-imaged gas giants.
