  The observed low densities of gas giant planets with a high equilibrium
temperature can be simulated in models when a fraction of the surface radiation
is deposited deeper in the interior. Meanwhile migration theories suggest that
hot Jupiters formed further away from their host-star and migrated inward. We
incorporate disk migration in simulations of the evolving interior of hot
Jupiters to determine whether migration has a long lasting effect on the
inflation of planets. We quantify the difference between the radius of a
migrated planet and the radius of a planet that formed in situ as the radius
discrepancy. We remain agnostic about the physical mechanism behind interior
heating, but assume it scales with the received stellar flux by a certain
fraction. We find that the change in irradiation received from the host-star
while the planet is migrating can affect the inflation and final radius of the
planet. Models with a high fraction of energy deposited in the interior ( > 5%)
show a significant radius discrepancy when the deposit is at higher pressures
than P=1 bar. For a smaller fraction of 1%, there is no radius discrepancy for
any deposit depth. We show that a uniform heating mechanism can cause different
rates of inflation, depending on the migration history. If the forthcoming
observations on mean densities and atmospheres of gas giants give a better
indication of a potential heating mechanism, this could help to constrain the
prior migration of such planets.
