The heater core is like a small radiator. The fluid from the hose gets pushed through a number of very small diameter tubes that have fins on the outside. That makes it a perfect place to collect gunk, just like the grid on the drain in the shower.

 

I am having the same problem with my 2002 Protege 5 heater. It takes about 20 plus min to get any sort of warm air. I don't have the foggiest of ideas on flushing my hoses. I don't have a high powered water hose, but I do have an air compressor. I also have the manual for the P5. Is there a video or more specifically, what key words would I likely use?

 

Flush heater core
flush cooling system.

Ericthecarguy has good videos on youtube.

If the heater core shows trouble it is best to flush the whole cooling system. It is not brand or model specific (unless you have a Pontiac Fiero).

 

Where on earth are the hoses that I need to flush? I've looked and looked at my manual, but of course they take away so much more in the picture vs. the actual engine.
Do you have a real picture you can show?

 

Hopefully this diagram helps a bit:



The heater unit is Nr. 2. In the car you would have to dive behind the engine, about in the middle and half ways down the fire wall. There will be 2 black hoses, about 1 1/2" in diameter that connect to the nipples in that triangular piece of the heater unit.
I cannot find a photo of an actual car showing this. In the engine bay you will only see the hoses going to the nipples. The heater box is hidden in the dash.