ABSTRACT The observed low densities of gas giant planets with a high equilibrium temperature (hot Jupiters) 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 disc 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 per cent) show a significant radius discrepancy when the deposit is at higher pressures than $P=1 \, \mathrm{bar}$. For a smaller fraction of 1 per cent, 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.