Yes the batteries are liquid cooled. The cooling process works gradually as the coolant temperature increases. On cold batteries, no coolant flows through electronics, motor, and batter pack. Once the temp rise, water pump starts and coolant starts flowing where required. There's a seven way valve present in the system that directs coolant flow.
On further temp increase, radiator fan kicks in to cool the coolant.
Other than that, in some BYD models, heat pump can further directly cool or heat up the battery pack.