The battery is big, so it has high thermal mass and lots of area for cooling. The motor is small. Motors can also easily be thermally limited. A permanent magnet motor that overheats will demagnetize and be destroyed. Induction motors and other non-permanent-magnet motors are less sensitive, but resistance goes up and metals and glues soften at higher temperature.
My understanding is that getting rid of waste heat is one of the main factors that limits how much power you can get out of an electric motor for any length of time. Less heat means you can get up a long steep hill without overheating (or causing the electronics to back off on the motor amperage to avoid damage).
The battery is big, so it has high thermal mass and lots of area for cooling. The motor is small. Motors can also easily be thermally limited. A permanent magnet motor that overheats will demagnetize and be destroyed. Induction motors and other non-permanent-magnet motors are less sensitive, but resistance goes up and metals and glues soften at higher temperature.