I have a 2001 F150 with a 5.4L engine. The heater core doesn't heat up. The hose from the front of the engine gets hot but the heat core and the other hose that goes behind the engine stays cold. The front hose is easy to access but the other hose looks like it goes behind the engine and can't see where it attaches to the engine. We would try to removed the hoses and try to flush the heater core but can only access the front hose. Where does the other hose connect and can it be easily removed. Pictures of hose connections would be an huge help.

 

Here is the view of my 2000 5.4.....this is a view from the back with the cab off.

 

My heater hasn't worked in years. I took it in once and they replaced a clogged hose and it worked for a couple days then it stopped heating again. I removed the replaced hose to see if it had clogged again but it had not.

 

You have a blockage somewhere else in the system. Get it flushed.