No 4/0 battery cable will not fit. The max is probably 6 awg.
The unit has a built in temp sensor. You can also use a wireless temp sensor (the Victron Smart Battery Sense) but because this charge controller does not have Bluetooth built-in you would also have to purchase the Bluetooth Dongle in addition.
For on-battery sensing it would be more economical to purchase the SmartSolar version of this controller with Built-in bluetooth and then add the Smart Battery Sense to have temperature sensing directly on the battery.