Really? Are you saying 7 mins of hard driving will render it literally unable to continue?

Perhaps getting down downvoted by people who expect Tesla may have thought about this. I remember reading the overheating was due to the regenerative braking trying to push power back into the battery so it was getting hard charged and discharged constantly and you couldn't switch off the charging. The bigger battery may be so you can switch off the regenerative braking.

It does. It will heat up. To quote a physics textbook: “Power transfer between a voltage source and an external load is at its most efficient when the resistance of the load matches the internal resistance of the voltage source.” IOW in the configuration where the power transfer is at its most efficient, battery has to dissipate as much thermal energy as motor(s) are consuming. Too much internal resistance and most of the thermal energy ends up in the battery. Too little, and your motors aren’t going to do their best. But in either case even with the load that’s not 100% matched, you do end up with a ton of heat dissipation in the battery when a heavy car like this is driven hard.