The invention relates to methods and systems for an internal combustion engine with a liquid-cooled cylinder head and a liquid-cooled cylinder block. The methods and systems are provided for separately providing liquid-cooling to a cylinder head and a cylinder block. In one example, a method includes selectively pumping coolant with a single pump to each of a first cylinder head coolant jacket and a cylinder block coolant jacket based on engine temperatures. The method further includes discharging coolant from the first cylinder head coolant jacket to a heating circuit line including a vehicle interior heater and discharging coolant from the cylinder block cooling jacket and back to the single pump.