Two cube$-$shaped tanks with a side length of $6$ meters are connected to each other. A pump in the lower connection circulates $120$ liters of water per minute. It is known that the pump works only against hydrostatic pressure. $100$w$/$m$^2$ heat enters from the side wall of tank B$.$ Find the time required for the water, which is initially $20$ degrees Celsius, to reach the saturated liquid form.