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Hot and Warm Jupiters (HJs&WJs) are gas-giant planets orbiting their hoststars at short orbital periods, posing a challenge to their efficient in-situformation. Therefore, most of the HJs&WJs are thought to have migrated from aninitially farther-out birth locations. Current migration models, i.edisc-migration (gas-dissipation driven) and eccentric-migration (tidalevolution driven), fail to produce the occurrence rate and orbital propertiesof HJs&WJs. Here we study the role of the thermal evolution and its coupling totidal evolution. We use the AMUSE, numerical environment, and MESA, planetaryevolution modeling, to model in detail the coupled internal and orbitalevolution of gas-giants during their eccentric-migration. In a companion paper,we use a simple semi-analytic model, validated by our numerical model, and runa population-synthesis study. We consider the initially inflated radii ofgas-giants (expected following their formation), as well study the effects ofthe potential slowed contraction and even re-inflation of gas-giants (due totidal and radiative heating) on the eccentric-migration. Tidal forces thatdrive eccentric-migration are highly sensitive to the planetary structure andradius. Consequently, we find that this form of inflated eccentric-migrationoperates on significantly (up to an order of magnitude) shorter timescales thanpreviously studied eccentric-migration models. Thereby, inflatedeccentric-migration gives rise to more rapid formation of HJs&WJs, higheroccurrence rates of WJs, and higher rates of tidal disruptions, compared withprevious eccentric migration models which consider constant ~Jupiter radii forHJ&WJ progenitors. Coupled thermal-dynamical evolution of eccentric gas-giantscan therefore play a key-role in their evolution.

Inflated Eccentric Migration of evolving gas giants II: Numerical methodology and basic concepts