hmm .. this is a toughie. Did you notice that when you first started the engine (when it was cold), that little to no water was entering the radiator from the top hose. Then after 10-15 minutes did you notice that the thermostat had opened, and water was clearly coming into the top of the radiator (from the top hose)?
Don't recall if you mentioned it before, but does the dashboard temp guage show the engine is heating up to the normal "running" temperature? Usually that is around 1/2 way up the guage, maybe to 2/3 up. i.e. Is the coolant reaching normal operating temps when the car has warmed up?
If all the above seems ok, about the only thing remaining it seems to me is something wrong with the heater core itself, the temp control valve, or the blower somehow is being prevented from blowing air across the heater core element. That could be caused by a faulty vent door somewhere under the dashboard which causes the airflow to bypass the heater core, even when you have "hot" selected. Because the hoses to the heater core indicate heat is entering and leaving as expected, my guess is a problem w/ the temp control valve or a faulty vent door. I'm not familiar w/your make/model so I don't even know if you have vent doors. But you almost certainly have a heat control valve. One thing you could do to test the heat control valvle idea is rig up an experiement somehow to see how much coolant was flowing through the heater core. More should go through when the heat control valve is set to "hot" than to "cold". You have to be careful not to affect the engine cooling when you do this though. Otherwise you may have a fixed heater but a dead engine.
Do you want to fix this yourself? I'ts going to be difficult to do unless you have the heating system diagrams you'll need to effect the diagnosis. You need the exact configuration of all the heating gadgets involved. Do you have the manufacturer's shop manual for this car? A Chiltons is good for tune ups and routine maintenance, but probably isn't enough for this problem. You need the shop manual to see all the heating/venting diagrams. If you don't already have one, it might pay to buy one. Or visit your local library. They probably don't have the shop manual, but they likely have the MOTOR manuals which mechanics use -- which sort of summarize the shop manual. If your library has the computer database service "AllData", that's a good alternative to the shop manual. If they have it, that's probably the first place to look.
In a pinch, most any good independent mechanic should be able to fix this for you.