The batteries/BMS can handle 200 amps charging and discharging......He is charging with 40 amps and is discharging at 60 amps max.......so they may rise a degree or so....stop worrying.....JUST DO IT!!!!!
This is not a car.....in a car you need the most watts per lb.(energy density).....so LIthium Ion batteries are used.....however, they are not as safe as Lithium Polymer (LifePo4)......In our homes we use LifePo4 because they are generally safer. What the car industry is looking for is even more energy density and even lighter and more safe.....they will get there.....then we can use these batteries with our inverter.
LifePo4 batteries are already very energy dense......a 200 amp hour AGM battery is typically 125 lbs......A 200 amp hour LIfePo4 battery is 49 lbs. The AGM battery is less than half the price.....but you cannot use all of its capacity and they only last less than half as long......They will actually cost you more over time and perform less good. LifePo4 is pretty darn good (for now)
Maybe you will come up with some other concern......My sweet child.....I will hold your hand as we cross the street....You will be safe.