Is there a valve that allows water to flow through the heater core, or does it flow all the time.

 

Has the radiator been replaced? If not, look down inside and see if the tubes are stopped up with fluffy stuff. Your core may be stopped up. Since the heater hoses are just warm, before you tear into the dash to replace the core, drain the radiator down a bit and unhook the hoses. Splice them together into a loop. Refill the coolant. Warm the engine up and see what the hoses do. If they get as hot as the upper hose, your core is stopped up. If there is a radiator shop near you, see if they can back flush the core. Sometimes you get lucky and this will open the core up. I did that once and drove the car for another 4 years with plenty of heat in the winter. Now, it's possible the core is weak and the back flush will blow a hole in it. Well, you were going to have to replace it anyway. Maybe they can do it at a reasonable cost. I've replaced heater cores before. I prefer not to. My arms aren't very thin and I have trouble working in the dash.

If the hoses in the loop still only get warm, your impellers on the water pump may be worn and you need a new pump. I'm thinking your core is stopped up rather then your water pump is bad.