Diagnosing no heat

[Formula413]

My car has little to no heat. I opened up the heater box today and felt the heater core, it was just barely warm to the touch with the engine at ~200*. Is there anything else I should check before I slap a new one in there? Could the old one be flushed effectively? I was looking at a diagram of the cooling system and I noticed there is a part on the hose leading to the core called a "flow restrictor", is that a mechanical part that could fail? Or just a fixed restrictor?