The valve on the hose allows coolant to flow through the heater core so if the core gets hot then the valve is working. If the whole core is getting hot then it is working and not plugged up and that would point me towards the blend door. When you change between hot and cold there is a door that is activated by either vacuum or a cable. If you look next to the heater core you will see a lever. See if when you switch from cold to hot if you can see the lever move.